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【349944】年山西省中考数学试题

时间:2025-03-05 22:03:42 作者: 字数:26720字
简介:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 山西省中考数学试题

I 选择题(共30分)

一、选择题(本大题共10个小题,每小题3分,共30分.在每个小题给出的四个选项中,只有一项符合题目要求,请选出并在答题卡上将该项涂黑)

1.计算 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的结果是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】根据有理数的除法法则计算即可,除以应该数,等于乘以这个数的倒数.

【详解】解:(-6÷- <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> =-6×-3=18.故选:C

【小结】本题考查了有理数的除法,熟练掌握运算法则是解题的关键.



2.自新冠肺炎疫情发生以来,全国人民共同抗疫,各地积极普及科学防控知识.下面是科学防控知识的图片,图片上有图案和文字说明,其中的图案是轴对称图形的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】根据轴对称图形的概念判断即可.

A、不是轴对称图形;
B
、不是轴对称图形;
C
、不是轴对称图形;
D
、是轴对称图形;
故选:D

【小结】本题考查了轴对称图形的概念,轴对称图形的关键是寻找对称轴,图形两部分折叠后可重合,如果一个图形沿着一条直线对折后两部分完全重合,这样的图形叫做轴对称图形,这条直线叫做对称轴.






3.下列运算正确 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】利用合并同类项、单项式除法、幂的乘方、单项式乘法的运算法则逐项判定即可.

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,故A选项错误;

B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,故B选项错误;

C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,故C选项正确;

D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,故D选项错误.

故答案为C

【小结】本题考查了合并同类项、单项式除法、积的乘方、单项式乘法等知识点,灵活应用相关运算法则是解答此类题的关键.


4.下列几何体都是由 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 个大小相同的小正方体组成的,其中主视图与左视图相同的几何体是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】分别画出四个选项中简单组合体的三视图即可.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 、左视图为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,主视图为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,左视图与主视图不同,故此选项不合题意;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 、左视图为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,主视图为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,左视图与主视图相同,故此选项符合题意;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 、左视图为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,主视图为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,左视图与主视图不同,故此选项不合题意;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 、左视图为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,主视图为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,左视图与主视图不同,故此选项不合题意;

故选B

【小结】此题主要考查了简单组合体的三视图,关键是掌握左视图和主视图的画法.



5.泰勒斯是古希腊时期的思想家,科学家,哲学家,他最早提出了命题的证明.泰勒斯曾通过测量同一时刻标杆的影长,标杆的高度。金字塔的影长,推算出金字塔的高度。这种测量原理,就是我们所学的(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

A. 图形的平移 B. 图形的旋转 C. 图形的轴对称 D. 图形的相似

【解析】根据在同一时刻的太阳光下物体的影长和物体的实际高度成比例即可判断;

根据题意画出如下图形:可以得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 即为金字塔的高度, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 即为标杆的高度,通过测量影长即可求出金字塔的高度

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 故选:D.

【小结】本题主要考查将实际问题数学化,根据实际情况画出图形即可求解.


6.不等式组 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的解集是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】先分别求出各不等式的解集,最后再确定不等式组的解集.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

由①得x3

由②得x5

所以不等式组的解集为x5

故答案为A

【小结】本题考查了解不等式组,掌握不等式的解法和确定不等式组解集的方法是解答本题的关键.





7.已知点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 都在反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的图像上,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的大小关系是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】首先画出反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,利用函数图像的性质得到当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的大小关系.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 反比例函数图像在第二、四象限,

观察图像:当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 时,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .故选A

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【小结】本题考查的是反比例函数的图像与性质,掌握反比例函数的图像与性质是解题的关键.












8.中国美食讲究色香味美,优雅的摆盘造型也会让美食锦上添花.图①中的摆盘,其形状是扇形的一部分,图②是其几何示意图(阴影部分为摆盘),通过测量得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 两点之间的距离为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,圆心角为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,则图中摆盘的面积是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】先证明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是等边三角形,求解 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,利用摆盘的面积等于两个扇形面积的差可得答案.

如图,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是等边三角形,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

所以则图中摆盘的面积 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 故选B

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【小结】本题考查的是扇形面积的计算,等边三角形的判定与性质,掌握以上知识是解题的关键.








9.竖直上抛物体离地面的高度 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 与运动时间 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 之间的关系可以近似地用公式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 表示,其中 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是物体抛出时离地面的高度, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是物体抛出时的速度.某人将一个小球从距地面 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的高处以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的速度竖直向上抛出,小球达到的离地面的最大高度为(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】将 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,利用二次函数的性质求出最大值,即可得出答案.

依题意得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,把 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 代入 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

故小球达到的离地面的最大高度为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 故选:C

【小结】本题考查了二次函数的性质的应用利用二次函数在对称轴处取得最值是解决本题关键属于基础题.


10.如图是一张矩形纸板,顺次连接各边中点得到菱形,再顺次连接菱形各边中点得到一个小矩形.将一个飞镖随机投掷到大矩形纸板上,则飞镖落在阴影区域的概率是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】连接菱形对角线,设大矩形的长=2a,大矩形的宽=2b,可得大矩形的面积,根据题意可得菱形的对角线长,从而求出菱形的面积,根据“顺次连接菱形各边中点得到一个小矩形”,可得小矩形的长,宽分别是菱形对角线的一半,可求出小矩形的面积,根据阴影部分的面积=菱形的面积-小矩形的面积可求出阴影部分的面积,再求出阴影部分与大矩形面积之比即可得到飞镖落在阴影区域的概率.

如图,连接EGFH,设AD=BC=2aAB=DC=2b,则FH=AD=2aEG=AB=2b

四边形EFGH是菱形,∴S菱形EFGH= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> =2ab

MOPN点分别是各边的中点,∴OP=MN= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> FH=aMO=NP= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> EG=b

四边形MOPN是矩形,∴S矩形MOPN=OP <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> MO=ab

S阴影= S菱形EFGH-S矩形MOPN=2ab-ab=ab

S矩形ABCD=AB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> BC=2a <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 2b=4ab,∴飞镖落在阴影区域的概率是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,故选B

II 非选择题(共90分)

二、填空题(本大题共5个小题,每小题3分,共15分)

11.计算: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ________

【解析】原式=2+2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> +3−2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> =5.

故答案为5.


12.如图是一组有规律的图案,它们是由边长相等的正三角形组合而成,第 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 个图案有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 个三角形,第 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 个图案有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 个三角形,第 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 个图案有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 个三角形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 按此规律摆下去,第 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 个图案有_______个三角形(用含 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的代数式表示).

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】由图形可知第1个图案有3+1=4个三角形,第2个图案有3×2+ 1=7个三角形,第3个图案有3×3+ 1=10个三角形...依此类推即可解答.

【详解】解:由图形可知:

1个图案有3+1=4个三角形,

2个图案有3×2+ 1=7个三角形,

3个图案有3×3+ 1=10个三角形,

...

n个图案有3×n+ 1=3n+1)个三角形.

故答案为(3n+1).

【小结】本题考查图形的变化规律,根据图形的排列、归纳图形的变化规律是解答本题的关键.









13.某校为了选拔一名百米赛跑运动员参加市中学生运动会,组织了 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 次预选赛,其中甲,乙两名运动员较为突出,他们在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 次预选赛中的成绩(单位:秒)如下表所示:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

由于甲,乙两名运动员的成绩的平均数相同,学校决定依据他们成绩的稳定性进行选拔,那么被选中的运动员是______

【答案】甲

【解析】直接求出甲、乙的平均成绩和方差,进而比较方差,方差小的比较稳定,从而得出答案.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> =12

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> =12

甲的方差为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

乙的方差为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

即甲的方差<乙的方差,∴甲的成绩比较稳定.故答案为甲.

【小结】本题考查了方差的定义.一般地,设n个数据, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的平均数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,则方差为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>












14.如图是一张长 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,宽 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的矩形铁皮,将其剪去两个全等的正方形和两个全等的矩形,剩余部分(阴影部分)可制成底面积 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是的有盖的长方体铁盒.则剪去的正方形的边长为______ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】根据题意设出未知数,列出三组等式解出即可.

【详解】设底面长为a,宽为b,正方形边长为x,

由题意得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

解得a=102x,b=6x,代入ab=24中得: (102x)(6x)=24,

整理得:2x211x+18=0

解得x=2x=9(舍去)

故答案为2

【小结】本题考查一元二次方程的应用,关键在于不怕设多个未知数,利用代数表示列出方程.














15.如图,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的中点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的长为_______

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】过点FFH⊥ACH,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,设FHx,由已知条件可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,利用相似三角形的性质:对应边的比值相等即可得到关于x的方程,解方程求出x的值,利用 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 即可得到DF的长.

【详解】如解图,过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的中点,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,由勾股定理得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【小结】本题考查了相似的判定和性质、以及勾股定理的运用,解题的关键是作垂直,构造相似三角形.



三、解答题(本大题共8个小题,共75分.解答应写出文字说明,证明过程或演算步骤)

16.1)计算: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

2)下面是小彬同学进行分式化简的过程,请认真阅读并完成相应任务.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 第一步

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 第二步

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 第三步

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>   第四步

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  第五步

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  第六步

任务一:填空:①以上化简步骤中,第_____步是进行分式的通分,通分的依据是____________________或填为_____________________________

_____步开始出现错误,这一步错误的原因是_____________________________________

任务二:请直接写出该分式化简后的正确结果;

任务三:除纠正上述错误外,请你根据平时的学习经验,就分式化简时还需要注意的事项给其他同学提一条建议.








【解析】

1)先分别计算乘方,与括号内的加法,再计算乘法,再合并即可得到答案;

2)先把能够分解因式的分子或分母分解因式,化简第一个分式,再通分化为同分母分式,按照同分母分式的加减法进行运算,注意最后的结果必为最简分式或整式.

1)原式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

2)任务一:

三;分式的基本性质;分式的分子与分母都乘(或除以)同一个不为零的整式,分式的值不变;

故答案为:三;分式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 基本性质;分式的分子与分母都乘(或除以)同一个不为零的整式,分式的值不变;

五;括号前是“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ”号,去掉括号后,括号里的第二项没有变号;

故答案为:五;括号前是“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ”号,去掉括号后,括号里的第二项没有变号;

任务二:

解; <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

任务三:

解:答案不唯一,如:最后结果应化为最简分式或整式;约分,通分时,应根据分式的基本性质进行变形;分式化简不能与解分式方程混淆,等.

【小结】本题考查的是有理数的混合运算,分式的化简,掌握以上两种以上是解题的关键.












17. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 月份,省城太原开展了“活力太原·乐购晋阳”消费暖心活动,本次活动中的家电消费券单笔交易满 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 元立减 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 元(每次只能使用一张)某品牌电饭煲按进价提高 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 后标价,若按标价的八折销售,某顾客购买该电饭煲时,使用一张家电消费券后,又付现金 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 元.求该电饭煲的进价.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】根据满 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 元立减 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 元可知,打八折后的总价减去128元是实际付款数额,即可列出等式.

设该电饭煲的进价为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

根据题意,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

答;该电饭煲的进价为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【小结】本题主要考察了打折销售知识点,准确找出它们之间的关系列出等式方程是解题关键.


18.如图,四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是平行四边形,以点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 为圆心, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 为半径的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 相切于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 相交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的延长线交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的度数.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【解析】连接OB,即可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,再由平行四边形得出∠BOC=90°,从而推出∠C=45°,再由平行四边形的性质得出∠A=45°,算出∠AOB=45°,再根据圆周角定理即可得出∠E=22.连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 相切于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是平行四边形, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是平行四边形, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【小结】本题考查圆周角定理、平行四边形的性质,关键在于根据条件结合性质得出角度的变换.

19. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 年国家提出并部署了“新基建”项目,主要包含“特高压,城际高速铁路和城市轨道交通, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 基站建设,工业互联网,大数据中心,人工智能,新能源汽车充电桩”等.《 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 新基建中高端人才市场就业吸引力报告》重点刻画了“新基建”中五大细分领域( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 基站建设,工业互联网,大数据中心,人工智能,新能源汽车充电桩)总体的人才与就业机会.下图是其中的一个统计图.

请根据图中信息,解答下列问题:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

1)填空:图中 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 年“新基建”七大领域预计投资规模的中位数是______亿元;

2)甲,乙两位待业人员,仅根据上面统计图中的数据,从五大细分领域中分别选择了“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 基站建设”和“人工智能”作为自己的就业方向,请简要说明他们选择就业方向的理由各是什么;

3)小勇对“新基建”很感兴趣,他收集到了五大细分领域的图标,依次制成编号为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的五张卡片(除编号和内容外,其余完全相同),将这五张卡片背面朝上,洗匀放好,从中随机抽取一张(不放回),再从中随机抽取一张.请用列表或画树状图的方法求抽到的两张卡片恰好是编号为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 基站建设)和 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> (人工智能)的概率.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

W G D R X









【解析】(1)根据中位数的定义判断即可.

(2)根据图象分析各个优势,表达出来即可.

(3)利用列表法或树状图的方法算出概率即可.

(1)将数据从小到大排列:100,160,200,300,300,500,640,中位数为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

故答案为:300

(2)解:甲更关注在线职位增长率,在“新基建”五大细分领域中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 年第一季度“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 基站建设”在线职位与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 年同期相比增长率最高;

乙更关注预计投资规模,在“新基建”五大细分领域中,“人工智能”在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 年预计投资规模最大

(3)解:列表如下:

第二张

第一张

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>


 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>


 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>


 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>


 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>


或画树状图如下:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

由列表(或画树状图)可知一共有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 种可能出现的结果,且每种结果出现的可能性都相同,其中抽到“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ”和“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ”的结果有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 种.

所以, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> (抽到“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ”和“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>) <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【小结】本题考查统计图的数据分析及概率计算,关键在于从图像中获取有用信息.


20.阅读与思考:下面是小宇同学的数学日记,请仔细阅读并完成相应的任务.

××× 星期日

没有直角尺也能作出直角

今天,我在书店一本书上看到下面材料:木工师傅有一块如图①所示的四边形木板,他已经在木板上画出一条裁割线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,现根据木板的情况,要过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 上的一点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,作出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的垂线,用锯子进行裁割,然而手头没有直角尺,怎么办呢?

办法一:如图①,可利用一把有刻度的直尺在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 上量出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,然后分别以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 为圆心,以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 为半径画圆弧,两弧相交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,作直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 必为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

办法二:如图②,可以取一根笔直的木棒,用铅笔在木棒上点出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 两点,然后把木棒斜放在木板上,使点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 与点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 重合,用铅笔在木板上将点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 对应的位置标记为点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,保持点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 不动,将木棒绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 旋转,使点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 落在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 上,在木板上将点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 对应的位置标记为点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .然后将 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 延长,在延长线上截取线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,得到点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,作直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

我有如下思考:以上两种办法依据的是什么数学原理呢?我还有什么办法不用直角尺也能作出垂线呢?

任务:

1)填空;“办法一”依据的一个数学定理是_____________________________________

2)根据“办法二”的操作过程,证明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

3)①尺规作图:请在图③的木板上,过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 作出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的垂线(在木板上保留作图痕迹,不写作法);

说明你的作法依据的数学定理或基本事实(写出一个即可)

【解析】(1)利用 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 说明△DCE是直角三角形,说明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,进而得出利用的原理是勾股定理逆定理即可;

2)由作图的方法可以得出: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,得出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,利用三角形内角和得出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,说明垂直即可;

3)①以点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 为圆心,任意长为半径画弧,与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 有两个交点,分别以这两个交点为圆心,以大于这两个交点之间的距离的一半为半径画弧,这两段弧交于一点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 即可;

到一条线段两个端点距离相等的点,在这条线段的垂直平分线上,即可说明垂直.

【详解】(1)勾股定理的逆定理(或如果三角形两边的平方和等于第三边的平方,那么这个三角形是直角三角形);

2)证明:由作图方法可知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

3)解:①如图,直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 即为所求;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

图③

答案不唯一,如:三边分别相等的两个三角形全等(或 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> );等腰三角形顶角的平分线、底边上的高、底边上的中线重合(或等腰三角形“三线合一”);到一条线段两个端点距离相等的点,在这条线段的垂直平分线上等.

【小结】本题主要考查了垂直的判定,熟练掌握说明垂直的方法是解决本题的关键.


21.图①是某车站的一组智能通道闸机,当行人通过时智能闸机会自动识别行人身份,识别成功后,两侧的圆弧翼闸会收回到两侧闸机箱内,这时行人即可通过.图②是两圆弧翼展开时的截面图,扇形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是闸机的“圆弧翼”,两圆弧翼成轴对称, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 均垂直于地面,扇形的圆心角 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,半径 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 与点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 在同一水平线上,且它们之间的距离为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

1)求闸机通道的宽度,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 之间的距离(参考数据: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> );

2)经实践调查,一个智能闸机的平均检票速度是一个人工检票口平均检票速度的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 倍, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 人的团队通过一个智能闸机口比通过一个人工检票口可节约 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 分钟,求一个智能闸机平均每分钟检票通过的人数.



















【分析】(1)连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,并向两方延长,分别交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> , <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的长度就是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 之间的距离,依据解直角三角形,即可得到可以通过闸机的物体的最大宽度;

2)设一个人工检票口平均每分钟检票通过的人数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 人,根据“一个智能闸机的平均检票速度是一个人工检票口平均检票速度的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 倍, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 人的团队通过一个智能闸机口比通过一个人工检票口可节约 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 分钟”列出分式方程求解即可;还可以设一个智能闸机平均每分钟检票通过的人数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 人,根据题意列方程求解.

【解析】连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,并向两方延长,分别交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

由点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 与点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 在同一水平线上, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 均垂直于地面可知, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,所以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的长度就是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 之间的距离.同时,由两圆弧翼成轴对称可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 之间的距离为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>


1)解法一:设一个人工检票口平均每分钟检票通过的人数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 人.

根据题意,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

解,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

经检验 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是原方程的解

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

答:一个智能闸机平均每分钟检票通过的人数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 人.

解法二:设一个智能闸机平均每分钟检票通过的人数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 人.

根据题意,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

经检验 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是原方程的解.

答:一个智能闸机平均每分钟检票通过的人数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 人.

【小结】本题考查了解直角三角形及列分式方程解应用题,关键是掌握含30度的直角直角三角形的性质.

22.综合与实践

问题情境:

如图①,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 为正方形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 内一点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,将 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 按顺时针方向旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> (点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的对应点为点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ),延长 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

猜想证明:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

1)试判断四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的形状,并说明理由;

2)如图②,若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,请猜想线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的数量关系并加以证明;

解决问题:

3)如图①,若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,请直接写出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的长.

【分析】(1)由旋转可知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,再说明 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 可得四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是矩形,再结合 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 即可证明;

2)过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,先根据等腰三角形的性质得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,再证 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,再结合 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 即可解答;

3)过EEG⊥AD,先说明∠1=∠2,再设EF=x、则BE=FE=EF=BE=xCE=AE=3+x,再在Rt△AEB中运用勾股定理求得x,进一步求得BEAE <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 长,然后运用三角函数和线段的和差求得DGEG的长,最后在Rt△DEG中运用勾股定理解答即可.

【解析】(1)四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是正方形

理由:由旋转可知: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是矩形.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是正方形;

2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

证明:如图,过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是正方形, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

3)如图:过EEG⊥AD,∴GE//AB,∴∠1=∠2

EF=x,则BE=FE=EF=BE=xCE=AE=3+x

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> Rt△AEB中,BE=xAE=x+3AB=15

AB2=BE2+AE2,即152=x2+x+32,解得x=-12(舍),x=9

BE=9,AE=12

sin∠1= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,cos∠1= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

sin∠2= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,cos∠2= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,∴AG=7.2,GE=9.6

DG=15-7.2=7.8,∴DE= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

【小结】本题考查了正方形的性质、旋转变换、勾股定理、解三角形等知识,综合应用所学知识是解答本题的关键.


23.综合与探究

如图,抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 两点(点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 在点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的左侧),与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 与抛物线交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 两点,与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

1)请直接写出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 两点的坐标及直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的函数表达式;

2)若点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是抛物线上的点,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的横坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 与直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,当点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的三等分点时,求点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标;

3)若点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴上的点,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,求点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标.

【分析】

1)令 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 两点的坐标,把 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标代入一次函数解析式可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的解析式;

2)根据题意画出图形,分别表示 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 三点的坐标,求解 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的长度,分两种情况讨论即可得到答案;

3)根据题意画出图形,分情况讨论:①如图,当点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴正半轴上时,记为点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .再利用相似三角形与等腰直角三角形的性质,结合勾股定理可得答案,②如图,当点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴负半轴上时,记为点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,再利用相似三角形与等腰直角三角形的性质,结合勾股定理可得答案.

【解析】(1)令 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,设直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的函数表达式为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 代入得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的函数表达式为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

2)解:如图,根据题意可知,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 与点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标分别为

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

分两种情况:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 时,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> (舍去)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 时,得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> (舍去)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 当点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 是线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的三等分点时,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

3)解: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

分两种情况:

如图,当点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴正半轴上时,记为点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

如图,当点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴负半轴上时,记为点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> ,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> .即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

由①可知, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 的坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a>


【小结】本题考查的是二次函数与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/755/" title="山西" class="c1" target="_blank">山西</a> <a href="/tags/1071/" title="山西省" class="c1" target="_blank">山西省</a> 轴的交点坐标,利用待定系数法求一次函数的解析式,平面直角坐标系中线段的长度的计算,同时考查了相似三角形的判定与性质,等腰直角三角形的性质,勾股定理的应用,特别是分类讨论的数学思想,掌握以上知识是解题的关键.


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