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【323500】2023九年级数学上册 第一章 特殊平行四边形检测题(新版)北师大版

时间:2025-01-16 18:41:17 作者: 字数:12246字
简介:


第一章 特殊平行四边形检测

(本检测题满分:120分,时间:120分钟)

  1. 选择题(每小题3分,共30分)

1. (2015•江苏连云港中考)已知四边形ABCD,下列说法正确的是( )

A.ADBCABDC时,四边形ABCD是平行四边形

B.ADBCABDC时,四边形ABCD是平行四边形

C.ACBDAC平分BD时,四边形ABCD是矩形

D.ACBDACBD时,四边形ABCD是正方形

2.2015·贵州安顺中考)如图,点O是矩形ABCD的中心,EAB上的点,折叠后,点B恰好与点O重合,若BC=3,则折痕CE的长为( )

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

2题图

A.2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> D.6

3.从菱形的钝角顶点向对角的两条边作垂线,垂足恰好是该边的中点,则菱形的内角中钝角的度数是( )

A.150° B. 135° C. 120° D. 100°

4.已知一矩形的两边长分别为10 cm15 cm,其中一个内角的平分线分长边为两部分,这两部分的长为( )

A.6 cm9 cm B. 5 cm10 cm C. 4 cm11 cm D. 7 cm8 cm

5.如图,在矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 分别为边 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的中点. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则图中阴影部分的面积为( )

A.3 B.4 C.6 D.8

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

5题图

6题图

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>


6.如图,在菱形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 等于( )

A.20 B.15 C.10 D.5

7.若正方形的对角线长为2 cm,则这个正方形的面积为( )

A.4  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> B.2  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

8.矩形、菱形、正方形都具有的性质是(  )

A.每一条对角线平分一组对角 B.对角线相等

C.对角线互相平分 D.对角线互相垂直

9.如图,将一个长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,宽为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的矩形纸片先按照从左向右对折,再按照从下向上的方向对折,沿所得矩形两邻边中点的连线(虚线)剪下(如图(1)),再打开,得到如图(2)所示的小菱形的面积为( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

9题图

10题图

1 2


10.如图是一张矩形纸片 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,若将纸片沿 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 折叠,使 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 落在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 上,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的对应点为点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> (  )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

  1. 填空题(每小题3分,共24分)

11.已知菱形的边长为6,一个内角为60°,则菱形的较短对角线的长是_________.

12.如图,在菱形ABCD中,∠B60°,点EF分别从点BD同时以同样的速度沿边BCDC向点C运动.给出以下四个结论:

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ;

② ∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ;

当点EF分别为边BCDC的中点时,△AEF是等边三角形;

当点EF分别为边BCDC的中点时,△AEF的面积最大.

上述正确结论的序号有 .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

13.如图,四边形ABCD是正方形,延长AB到点E,使 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则∠BCE的度数是 .


14.如图,矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的两条对角线交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的垂线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,分别交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,已知△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的周长为24 cm,则矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的周长是 cm.

15.2015·贵州安顺中考)如图,正方形ABCD的边长为4EBC上的一点,BE=1FAB上的一点,AF=2PAC上一个动点,则PF+PE的最小值为 .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

15题图

16.已知菱形的周长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,一条对角线长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则这个菱形的面积为_________.

17.如图,矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的对角线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则图中五个小矩形的周长之和为_______.

组合 169  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

18题图

18. 2015·上海中考)已知E是正方形ABCD的对角线AC上一点,AEAD,过点EAC的垂线,交边CD于点F,那么∠FAD________度.



、解答题(共66分)

19.8分)如图,在△ABC中,AB=ACAD是△ABC外角的平分线,已知∠BAC=∠ACD.

1)求证:△ABC≌△CDA

2)若∠B=60°,求证:四边形ABCD是菱形.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

20.8分)如图,在ABCD中,EBC边上的一点,连接AEBDAE=AB.

1)求证:∠ABE=∠EAD

2)若∠AEB=2∠ADB,求证:四边形ABCD是菱形.

21.8分)(2015·贵州安顺中考)如图,已知点D在△ABCBC边上,DEACABEDFABACF.

1)求证:AE=DF.

2)若AD平分∠BAC,试判断四边形AEDF的形状,并说明理由.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

21题图

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

22.8分)如图,正方形ABCD的边长为3EF 分别是ABBC边上的点,且∠EDF=45°.将△DAE绕点D逆时针旋转90°,得到△DCM.

1)求证:EF=FM

2)当AE=1时,求EF的长.


23.8分)如图,在矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 相交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> . <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,求∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的度数.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

24.8分)如图所示,在矩形ABCD中,EF分别是边ABCD上的点,AECF,连接EFBFEF与对角线AC交于点O,且BEBF,∠BEF2∠BAC.

1)求证:OEOF

2)若BC <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,求AB的长.

25.(8)已知:如图,在四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 平分∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的中点.试说明: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 互相垂直平分.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 组合 205  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

26.(10) 如图,在△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 中,∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的垂直平分线 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,交 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 上,且 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

(1)求证:四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是平行四边形.

(2)当∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 满足什么条件时,四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是菱形?并说明理由.










第一章 特殊平行四边形检测参考答案

一、选择题

1.B 解析:一组对边平行,另一组对边相等的四边形可能是等腰梯形,故A项错误;两组对边分别相等的四边形一定是平行四边形,故B项正确;对角线相等且一条对角线平分另一条对角线的四边形不一定是矩形,故C项错误;对角线相等且互相垂直的四边形不一定是正方形,故D项错误.

2. A 解析根据图形折叠的性质可得:∠BCE=ACE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ACB,∠B=COE=90°BC=CO= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> AC,所以∠BAC=30°,所以∠BCE=ACE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ACB=30°.因为BC=3,所以CE=2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

3.C 解析如图,连接AC.在菱形ABCD中,AD=DC,AECD AFBC,因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以AECD的中垂线,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以△ADC是等边三角形,所以∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 60°,从而∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 120°.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

4.B 解析:如图,在矩形ABCD中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 10 cm <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 15 cm <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的平分线,则∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> C.AEBC得∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>AEB,所以∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>AEB,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 10 cmED=AD-AE=15-10=5(cm),故选B.

5.B 解析因为矩形ABCD的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

所以阴影部分的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,故选B

6组合 212 . D 解析在菱形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 中,由∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,得 ∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .又∵  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

∴ △ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是等边三角形,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

7.B 解析如图,在正方形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以正方形的面积为2  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,故选B.

8.C

9.A 解析由题意知ACBD, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 4  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 5  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

10.A 解析由折叠知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 为正方形,

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

二、填空题

11.6 解析:较短的对角线将菱形分成两个全等的等边三角形,所以较短对角线的长为6.

12.①②③ 解析因为四边形ABCD为菱形,所以AB <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> CD,∠B=∠DBE=DF,所以△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ≌△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以AE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> AF,①正确.

CB=CDBE=DF,CE=CF,所以∠CEF=∠CFE,②正确.

EF分别为BCCD的中点时,BE=DF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> BC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> DC.连接ACBD,知△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 为等边三角形,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .因为ACBD,所以∠ACE=60°,∠CEF=30° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 ∠AEF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .由①知AE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> AF,故△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 为等边三角形,③正确.

设菱形的边长为1,当点EF分别为边BCDC的中点时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,而当点EF分别与点BD重合时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,故④错.

13.22.5° 解析:由四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是正方形,得∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .5°,所以∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

1


4.48 解析:由矩形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,又 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 垂直平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .已知△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的周长为24 cm,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

所以矩形ABCD的周长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

15. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 解析如图,作E关于直线AC的对称点E,则BE=DE,连接EF,则EF即为所求,过FFGCDG

RtEFG中,

GE′=CD-DE′-CG=CD-BE-BF=4-1-2=1GF=4

所以EF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

15题答图

16.96 解析因为菱形的周长是40,所以边长是10

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>
图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .根据菱形的性质,有 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

所以  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

17. 28 解析:由勾股定理, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> . <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 所以五个小矩形的周长之和为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

18.22.5 解析:由四边形ABCD是正方形,可知∠BAD=∠D=90°,∠CAD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>BAD=45°.

FEAC,可知∠AEF=90°.

Rt△ABCRt△ADC中,AE=ADAF=AF

Rt△AEF≌Rt△ADFHL),

∴ ∠FAD=∠FAE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>CAD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ×45°=22.5°.

三、解答题

19.证明:1)∵ AB=AC,∴ ∠B=∠ACB,∴ ∠FAC=∠B+∠ACB=2∠BCA.

AD平分∠FAC,∴ ∠FAC=2∠CAD,∴ ∠CAD=∠ACB.

在△ABC和△CDA中,∠BAC=∠DCA ACAC,∠DAC=∠ACB

∴ △ABC≌△CDA.

2)∵ ∠FAC=2∠ACB,∠FAC=2∠DAC,∴ ∠DAC=∠ACB,∴ ADBC.

∵ ∠BAC=∠ACD,∴ ABCD,∴ 四边形ABCD是平行四边形.

∵ ∠B=60°AB=AC,∴ △ABC是等边三角形,

AB=BC,∴ 平行四边形ABCD是菱形.

20.证明:1)在ABCD中,ADBC,∴ ∠AEB=∠EAD.

AE=AB,∴ ∠ABE=∠AEB,∴ ∠ABE=∠EAD.

2)∵ ADBC,∴ ∠ADB=∠DBE.

∵ ∠ABE=∠AEB,∠AEB=2∠ADB,∴ ∠ABE=2∠ADB

∴ ∠ABD=∠ABE-∠DBE=2∠ADB-∠ADB=∠ADB,∴ AB=AD.

又∵ 四边形ABCD是平行四边形,∴ 四边形ABCD是菱形.

21.解:1)证明:因为DEACDFAB

所以四边形AEDF是平行四边形,

所以AE=DF.

2)解:若AD平分∠BAC,则四边形AEDF是菱形,理由如下:

因为DEACDFAB

所以四边形AEDF是平行四边形,且∠BAD=FDA.

AD平分∠BAC,所以∠BAD=DAF

所以∠DAF=FDA

所以AF=DF

所以平行四边形AEDF为菱形.

22.1证明:∵ △DAE逆时针旋转90°得到△DCM,∴ ∠FCM=FCD+DCM=180°
FCM三点共线,DE=DM,∠EDM=90°,∴ ∠EDF+FDM=90°.
∵ ∠EDF=45°,∴ ∠FDM=EDF=45°.
在△DEF和△DMF中,DE=DM,∠EDF=MDFDF=DF

∴ △DEF≌△DMFSAS),∴ EF=MF.

2解:EF=MF=x,∵ AE=CM=1,且BC=3,∴ BM=BC+CM=3+1=4

BF=BMMF=BMEF=4x.

EB=ABAE=31=2,在RtEBF中,

由勾股定理得EB2+BF2=EF2,即22+4x2=x2
解得:x= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,即EF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

23.解:因为  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

又知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 为等边三角形,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

所以△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 为等腰直角三角形,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> =75°.

24.1证明:四边形ABCD是矩形,∴ ABCD.

∴ ∠OAE=∠OCF.

又∵ OA=OC, ∠AOE=∠COF,∴ △AEO≌△CFOASA.∴ OE=OF.

2:连接BO.∵ BE=BF,∴ △BEF是等腰三角形.

又∵ OE=OF,∴ BOEF,且∠EBO=∠FBO.∴ ∠BOF=90°.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

四边形ABCD是矩形,∴ ∠BCF=90°.

又∵ ∠BEF=2∠BAC,∠BEF=∠BAC+∠EOA,

∴ ∠BAC=∠EOA.∴ AE=OE.

AE=CF,OE=OF,∴ OF=CF.

又∵ BF=BF,∴ Rt△BOF≌Rt△BCFHL.

∴ ∠OBF=∠CBF.∴ ∠CBF=∠FBO=∠OBE.

∵ ∠ABC=90°,∴ ∠OBE=30°.∴ ∠BEO=60°.∴ ∠BAC=30°.

Rt△BAC中,∵ BC=2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴ AC=2BC=4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

AB= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

点拨:证明线段相等的常用方法有以下几种:①等腰三角形中的等角对等边;②全等三角形中的对应边相等;③线段垂直平分线的性质;④角平分线的性质;⑤勾股定理;⑥借助第三条线段进行等量代换.

25.解:如图,连接 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>ABAC,∴ ∠BAC=90°.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

因为在Rt <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的中点,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>Rt△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 的斜边BC上的中线,

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

ADBC,所以四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是平行四边形.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,所以平行四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是菱形,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 互相垂直平分.

26.1证明:由题意知∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴ ∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴ ∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>AEF =EAC =ECA .

又∵  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴ △ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ≌△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴ 四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是平行四边形 .

2解:当∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 时,四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是菱形 .理由如下:

∵ ∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 垂直平分 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> .

又∵  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> ,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a>

平行四边形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/58/" title="平行" class="c1" target="_blank">平行</a> <a href="/tags/82/" title="平行四边形" class="c1" target="_blank">平行四边形</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/915/" title="特殊" class="c1" target="_blank">特殊</a> 是菱形.




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