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【330500】第1章检测题及答案解析

时间:2025-02-09 11:35:14 作者: 字数:9108字

1章 直角三角形检测题

(本检测题满分:100分,时间:90分钟)

一、选择题(每小题3分,共24分)

1.如图所示 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 平分∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,垂足分别为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,下列结论正确 是(

A. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>     B. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

C. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>   D. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

DrawObject1

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>







2 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .如图所示,有两棵树,一棵高10 m,另一棵高4 m,两树相距8 m.一只小鸟从一棵树的树梢飞到另一棵树的树梢,问小鸟至少飞行( )

A.8 m B.10 m

C.12 m D.14 m

3.如图所示,已知 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,下列条件能使△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ≌△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的是(  )

A. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> B. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

C. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> D. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 三个答案都是

4.一直角三角形的两边长分别为34,则第三边的长为( )

A.5 B. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

C.5 D.5 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

5.如图所示,一棵树在一次强台风中,从离地面 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 处折断,倒下的部分与地面成 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 角,这棵树在折断前的高度是(  )

A. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> B. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> C. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> D. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>







6.如图所示,在△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 上, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的中点, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 相交于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,且 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .若 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,则 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> (  )

A. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> B. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> C. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> D. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

7.(201浙江湖州中考)如图,已知在△ABC中,CDAB边上的高线,BE平分∠ABC,交CD于点EBC5DE=2,则△BCE的面积等于( )

A.10 B.7

C.5 D.4

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>




7

8.2015·广西桂林中考)下列各组线段能构成直角三角形的一组是(  )

A.304050 B.71213 C.5912 D.346

二、填空题(每小题3分,共24分)

9.若直角三角形的两直角边长为ab,且满足 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,则该直角三角形的斜边长为 .

10.在△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,则 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> _______.

11.有一组勾股数,知道其中的两个数分别是178,则第三个数是 .

12.如图所示, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 是△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的角平分线, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点F,连接 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,则 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的位置关系是      .


DrawObject2


 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>






13.(长沙中考)如图所示BDABC的平分线,点PBD上的一点,PEBA于点EPE4 cm,则点P到边BC的距离为________cm.

1DrawObject3 4.如图所示, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 是∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的平分线, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,则关于直线 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 对称的三角形共有_______对.

15.如图所示,在Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 平分 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,交 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,且 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,则点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的距离是________.

16.如图,学校有一块长方形花圃,有极少数人为了避开拐角走“捷径”,在花圃内走出了一条“路”,他们仅仅少走了________步路(假设2步为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ),却踩伤了花草.


 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

三、解答题(共52分)

17.6)若△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 三边满足下列条件,判断△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 是不是直角三角形,并说明哪个角是直角.

1 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

2 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

18.6)若三角形的三个内角的比是 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,最短边长为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,最长边长为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

求:(1)这个三角形各角的度数;

2)另外一边长的平方.

19.(6)如图所示,在△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

求证: <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

组合 88

DrawObject4







20.6分)如图所示, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 是∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 内的一点, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,垂足分别为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

求证:(1 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ;(2)点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 在∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的平分线上.

21.(6) 2015·湖北孝感中考我们把两组邻边相等的四边形叫做“筝形”,如图,四边形ABCD是一个筝形,其中AB=CB,AD=CD.对角线AC,BD相交于点OOEAB,OFCB,垂足分别是EF.求证:OE=OF.

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> DrawObject5

21题图


22.(6)如图所示 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 为△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的高, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 上一点, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,且有 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

求证: <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

23.(8)已知:在△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的中点,点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 边上一点.

1 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 垂直于 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,交 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> (如图①),求证: <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

2 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 垂直于 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,垂足为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,交 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的延长线于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> (如图②),找出图中与 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 相等的线段,并证明.

DrawObject6



 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>







24.8)如图,折叠长方形的一边 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,使点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 落在 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 边上的点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 处, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> cm <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> cm

:(1 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的长;2 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的长.









1章 直角三角形检测题参考答案

1.A 解析:由 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 平分∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,知 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 故选项A正确.

2.B 解析:根据“两点之间线段最短”可知:小鸟沿着两棵树的树梢进行直线飞行,所飞行的路程最短,运用勾股定理可将两树梢之间的距离求出.

如图所示,设大树高AB=10 m,小树高CD=4 m.

连接AC,过点CCEAB于点E,则四边形EBDC是长方形.

EB=4 mEC=8 mAE=AB-EB=10-4=6(m).

RtAECAC=  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> = <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 10(m).

3.D 解析:添加A选项中条件可用“ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ”判定两个三角形全等;添加B选项中条件可用“ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ”判定两个三角形全等;添加C选项中条件可用“ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ”判定两个三角形全等,故选D

4.D 解析:当已知的两边均为直角边时,由勾股定理,得第三边长为5;当4为斜边长时,由勾股定理,得第三边长为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

点拨:本题中没有指明哪个是直角边哪个是斜边,故应该分情况进行分析.注意不要漏解.

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>







5.B 解析:如图,在Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中,∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,所以大树的高度为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .故选B

6.C 解析:因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .故选C

7.C 解析:过点EEFBC,垂足为F,根据角平分线上的点到角的两边的距离相等可得EDEF2,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,故选C.

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

7题答图

8.A 解析:选项A中,∵  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 2 500 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 2 500,∴  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,∴ 30,40,50能构成直角三角形;

在选项B中,∵  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 193 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 169,∴  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,∴ 7,12,13不能构成直角三角形;

在选项C中,∵  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 106 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 144,∴  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,∴ 5,9,12不能构成直角三角形;

在选项D中,∵  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 25 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 36,∴  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,∴ 3,4,6不能构成直角三角形.故选A.

9.5 解析:∵  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,解得 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

直角三角形的两直角边长为ab

该直角三角形的斜边长为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

点拨:本题考查了勾股定理、非负数的性质、绝对值和算术平方根的意义.

1 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 0. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 解析:如图所示,因为等腰三角形底边上的高、中线以及顶角平分线三线合一,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> cm

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

11.15 解析:设第三个数是 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 为最长边,则 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,不是正整数,不符合题意;

17为最长边,则 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,三边长都是整数,能构成勾股数,符合题意.故答案为15

12. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 垂直平分 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>   解析:因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 是△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的角平分线, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> B于点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 于点F,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 所以Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ≌Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 是△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的角平分线,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 垂直平分 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

13.4 解析:本题考查了角平分线的性质. 角平分线上的点到角两边的距离相等, P到边BC的距离等于PE的长度.

1DrawObject7 4. <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 解析:△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 和△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 和△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 和△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 和△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 4.

15.3 解析:如图,过 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 点作 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 平分 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的距离 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

16.4 解析:在Rt <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 少走了  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

17. 解:(1)因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

根据三边满足的条件,可以判断△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 是直角三角形,其中 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 为直角.

2)因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

根据三边满足的条件,可以判断 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 是直角三角形,其中∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 为直角.

18.解:(1)因为三个内角的比是 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以设三个内角的度数分别为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,得 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以三个内角的度数分别为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

2由(1可知三角形为直角三角形,

则一条直角边长为1,斜边长为2.

设另外一条直角边长为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,则 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,即 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

所以另外一条边长的平方为3.

19.证明:在△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中,因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

又因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

2 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 0.证明:(1)连接 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

2)因为Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> HL),

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 在∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的平分线上.

21.证明:在△ABD和△CBD中,

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ABD≌△CBD(SSS),

ABD=CBD, BD平分∠ABC.

又∵ OEAB,OFCB, OE=OF.

22.证明:在Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 和在Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中,

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 所以Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ≌Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

又在Rt△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以∠AEB=90°,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

23.1)证明:因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 垂直于 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

又因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> , <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

又因为点 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的中点所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ≌△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

(2)解: <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .证明如下

在△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中,因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> , <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,∠ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,即 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 为等腰直角三角形斜边上的中线,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> , <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> , <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,

所以△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ≌△ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

24. 解:(1)由题意可得 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

Rt <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中,因为  <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

所以 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

2)由题意可得 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

可设 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的长为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,则 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> .

Rt <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 中,由勾股定理

 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>

解得 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> ,即 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> 的长为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a>