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【327803】2023年广东省中考数学真题

时间:2025-01-20 20:18:35 作者: 字数:16642字
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2023年广东省中考数学真题

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评卷人

得分




一、选择题

1.负数的概念最早出现在我国古代著名的数学专著《九章算术》中,如果把收入5元记作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 元,那么支出5元记作(     
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
B
0
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

2.下列出版社的商标图案中,是轴对称图形的为(     
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    

3.2023528日,我国自主研发的C919国产大飞机商业首航取得圆满成功,C919可储存约186000升燃油,将数据186000用科学记数法表示为(     
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

4.如图,街道 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 平行,拐角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,则拐角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>      
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

5.计算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的结果为(     
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

6.我国著名数学家华罗庚曾为普及优选法作出重要贡献,优选法中有一种0.618法应用了(     
A
.黄金分割数
B
.平均数
C
.众数
D
.中位数

7.某学校开设了劳动教育课程.小明从感兴趣的“种植”“烹饪”“陶艺”“木工”4门课程中随机选择一门学习,每门课程被选中的可能性相等,小明恰好选中“烹饪”的概率为(     
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

8.一元一次不等式组 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的解集为(     )
A
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

9.如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的直径, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>      
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

10.如图,抛物线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 经过正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的三个顶点ABC,点B <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 轴上,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的值为(     
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
B
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
C
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

评卷人

得分




二、填空题

11.因式分解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ______.

12.计算 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> _________

13.某蓄电池的电压为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,使用此蓄电池时,电流 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> (单位: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> )与电阻 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> (单位: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> )的函数表达式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,当 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的值为_______ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

14.某商品进价4元,标价5元出售,商家准备打折销售,但其利润率不能少于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,则最多可打_______折.

15.边长分别为1064的三个正方形拼接在一起,它们的底边在同一直线上(如图),则图中阴影部分的面积为_______
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    

评卷人

得分




三、解答题

16.1)计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
2)已知一次函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的图象经过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 与点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,求该一次函数的表达式.

17.某学校开展了社会实践活动,活动地点距离学校 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,甲、乙两同学骑自行车同时从学校出发,甲的速度是乙的 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 倍,结果甲比乙早到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,求乙同学骑自行车的速度.

18.2023530日,神舟十六号载人飞船发射取得圆满成功,3名航天员顺利进驻中国空间站,如图中的照片展示了中国空间站上机械臂的一种工作状态,当两臂 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,两臂夹角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 时,求AB两点间的距离.(结果精确到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,参考数据 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> )
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    

19.如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
(1)实践与操作:用尺规作图法过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 边上的高 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> (保留作图痕迹,不要求写作法)
(2)
应用与计算:在(1)的条件下, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的长.

20.综合与实践
主题:制作无盖正方体形纸盒
素材:一张正方形纸板.
步骤1:如图1,将正方形纸板的边长三等分,画出九个相同的小正方形,并剪去四个角上的小正方形;
步骤2:如图2,把剪好的纸板折成无盖正方体形纸盒.
猜想与证明:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
(1)直接写出纸板上 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 与纸盒上 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的大小关系;
(2)
证明(1)中你发现的结论.

21.小红家到学校有两条公共汽车线路,为了解两条线路的乘车所用时间,小红做了试验,第一周(5个工作日)选择A线路,第二周(5个工作日)选择B线路,每天在固定时间段内乘车2次并分别记录所用时间,数据统计如下:(单位:min)
数据统计表

试验序号

1

2

3

4

5

6

7

8

9

10

A线路所用时间

15

32

15

16

34

18

21

14

35

20

B线路所用时间

25

29

23

25

27

26

31

28

30

24

数据折线统计图
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
根据以上信息解答下列问题:


平均数

中位数

众数

方差

A线路所用时间

22

a

15

63.2

B线路所用时间

b

26.5

c

6.36

(1)填空: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> __________ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ___________ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ___________
(2)
应用你所学的统计知识,帮助小红分析如何选择乘车线路.

22.综合探究
如图1,在矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 相交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的对称点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
(1)求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
(2)
以点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 为圆心, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 为半径作圆.
如图2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 相切,求证: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
如图3 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 相切, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的面积.

23.综合运用
如图1,在平面直角坐标系中,正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的顶点A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 轴的正半轴上,如图2,将正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 绕点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 逆时针旋转,旋转角为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 交直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 轴于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>       
(1)当旋转角 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 为多少度时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ;(直接写出结果,不要求写解答过程)
(2)
若点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的长;
(3)
如图3,对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 轴于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,交直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,将 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的面积分别记为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的函数表达式.

参考答案

1.A

【解析】
根据相反数的意义可进行求解.
解:由把收入5元记作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 元,可知支出5元记作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 元;
故选A

2.A

【解析】
根据轴对称图形的概念:一个图形沿一条直线折叠,直线两旁部分能够完全重合的图形;由此问题可求解.
解:符合轴对称图形的只有A选项,而BCD选项找不到一条直线能使直线两旁部分能够完全重合;
故选A

3.B

【解析】
科学记数法的表示形式为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的形式,其中 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> n为整数.确定n的值时,要看把原数变成a时,小数点移动了多少位,n的绝对值与小数点移动的位数相同.当原数绝对值大于或等于10时,n是正整数;当原数的绝对值小于1时,n是负整数.
解:将数据186000用科学记数法表示为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故选B

4.D

【解析】
根据平行线的性质可进行求解.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故选D

5.C

【解析】
根据分式的加法运算可进行求解.
解:原式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故选C

6.A

【解析】
根据黄金分割比可进行求解.
解:0.618为黄金分割比,所以优选法中有一种0.618法应用了黄金分割数;
故选A

7.C

【解析】
根据概率公式可直接进行求解.
解:由题意可知小明恰好选中“烹饪”的概率为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故选C

8.D

【解析】
第一个不等式解与第二个不等式的解,取公共部分即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
解不等式 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
结合 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 得:不等式组的解集是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故选:D

9.B

【解析】
根据圆周角定理可进行求解.
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的直径,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故选B

10.B

【解析】
连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,交y轴于点D,根据正方形的性质可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,然后可得点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,进而代入求解即可.
解:连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,交y轴于点D,如图所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 时,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是正方形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故选B

11. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

【解析】
利用平方差公式进行因式分解即可得.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故答案为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

12.6

【解析】
利用二次根式的乘法法则进行求解即可.
解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故答案为:6

13.4

【解析】
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 代入 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 中计算即可;
解:∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故答案为:4

14.8.8

【解析】
设打x折,由题意可得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,然后求解即可.
解:设打x折,由题意得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故答案为8.8

15.15

【解析】
根据正方形的性质及相似三角形的性质可进行求解.
解:如图,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
由题意可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故答案为15

16.1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ;(2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

【解析】
1)先求出立方根及有理数的乘方运算,绝对值的化简,然后计算加减法即可;
2)将两个点代入解析式求解即可.
解:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
2)∵一次函数 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的图象经过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 与点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
代入解析式得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
一次函数的解析式为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

17.乙同学骑自行车的速度为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 千米/分钟.

【解析】
设乙同学骑自行车的速度为x千米/分钟,则甲同学骑自行车的速度为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 千米/分钟,根据时间=路程÷速度结合甲车比乙车提前10分钟到达,即可得出关于x的分式方程,解之并检验后即可得出结论.
解:设乙同学骑自行车的速度为x千米/分钟,则甲同学骑自行车的速度为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 千米/分钟,
根据题意得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
经检验, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是原方程的解,且符合题意,
答:乙同学骑自行车的速度为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 千米/分钟.

18. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

【解析】
连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,作作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> D,由等腰三角形“三线合一”性质可知, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 中利用 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,继而求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 即可.
解:连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,作 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> D
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 边上的中线,也是 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的角平分线,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
答:AB两点间的距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

19.(1)见解析
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

【解析】
1)根据过直线外一点作已知直线的垂线的方法作图即可,可用圆规以点D为圆心,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 上找到两个点到点D的距离相等,再分别以这两个点为圆心,相等且大于这两点距离的一半为半径画弧,再找到一个到这两个点的距离相等的点,连接最后得到的点与点D所得线段所在的直线就是高 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 所在的直线,据此画图即可;
2)先利用 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 度角的余弦值求出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,再由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 计算即可.
1)解:依题意作图如下,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 即为所求作的高:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
2)∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 边上的高,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

20.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
(2)
证明见解析.

【解析】
1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 均是等腰直角三角形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
2)证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是等腰直角三角形即可.
1)解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
2)证明:连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
设小正方形边长为1,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 为等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 为等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

21.(1)1926.825
(2)
见解析

【解析】
1)根据中位数定义将A线路所用时间按从小到大的顺序排列,求中间两个数的平均数即为A线路所用时间的中位数a,利用平均数的定义求出B线路所用时间的平均数b,找出B线路所用时间中出现次数最多的数据即为B线路所用时间的众数c,从而得解;
2)根据四个统计量分析,然后根据分析结果提出建议即可.
1)解:将A线路所用时间按从小到大顺序排列得:14151516182021323435,中间两个数是1820
∴A
线路所用时间的中位数为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
由题意可知B线路所用时间得平均数为:  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
∵B
线路所用时间中,出现次数最多的数据是25,有两次,其他数据都是一次,
∴B
线路所用时间的众数为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
故答案为:1926.825
2)根据统计量上来分析可知,A线路所用时间平均数小于B线路所用时间平均数线路,A线路所用时间中位数也小于B线路所用时间中位数,但A线路所用时间的方差比较大,说明A线路比较短,但容易出现拥堵情况,B线路比较长,但交通畅通,总体上来讲A路线优于B路线.
因此,我的建议是:根据上学到校剩余时间而定,如果上学到校剩余时间比较短,比如剩余时间是21分钟,则选择A路线,因为A路线的时间不大于21分钟的次数有7次,而B路线的时间都大于21分钟;如果剩余时间不短也不长,比如剩余时间是31分钟,则选择B路线,因为B路线的时间都不大于31分钟,而A路线的时间大于31分钟有3次,选择B路线可以确保不迟到;如果剩余时间足够长,比如剩余时间是36分钟,则选择A路线,在保证不迟到的情况,选择平均时间更少,中位数更小的路线.

22.(1)见解析
(2)①
见解析;② <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

【解析】
1)由点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的对称点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 可知点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的中点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,从而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的中位线,继而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,从而证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
2)①过点O <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点F,延长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点G,先证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,由 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 相切,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,继而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,从而证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的角平分线,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,利用直角三角形两锐角互余得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,从而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,最后利用含 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 度角的直角三角形的性质得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
先证明四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是正方形,得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,再利用 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的中位线得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,从而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,再利用平行线的性质得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,从而证明 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是等腰直角三角形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,求得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,从而得到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
1)∵点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的对称点为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的中点, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
又∵四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是矩形,
O <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的中点,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的中位线,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
2)①过点O <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点F,延长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点G,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是矩形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 相切, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 为半径, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的角平分线,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
解得: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
过点O <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点H
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 相切,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是矩形,
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是正方形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的中位线,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
又∵ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 是等腰直角三角形, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 的面积为: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

23.(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
(2)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
(3)
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>

【解析】
1)根据正方形的性质及直角三角形全等的判定及性质得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,再由题意得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,即可求解;
2)过点A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 轴,根据勾股定理及点的坐标得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,再由相似三角形的判定和性质求解即可;
3)根据正方形的性质及四点共圆条件得出OCFN四点共圆,再由圆周角定理及等腰直角三角形的判定和性质得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,过点N <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点G,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点Q,利用全等三角形及矩形的判定和性质得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,结合图形分别表示出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> ,再由等腰直角三角形的性质即可求解.
1)解:∵正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 交直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
2)过点A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 轴,如图所示:
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
3)∵正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
直线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
OCFN四点共圆,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 为等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
过点N <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点G,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 于点Q
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>    
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 为矩形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a> 为等腰直角三角形,
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/117/" title="广东" class="c1" target="_blank">广东</a> <a href="/tags/323/" title="广东省" class="c1" target="_blank">广东省</a>