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【323441】2023九年级数学上册 第23章 图形的相似检测题2(含解析)(新版)华东师大版

时间:2025-01-16 18:34:45 作者: 字数:10491字
简介:


23章 图形的相似检测题

(本检测题满分:120分,时间:120分钟)

一、选择题(每小题2分,共24分)

1.下列四组图形中,不是相似图形的是( )

组合 1276





2.如图,为估算某河的宽度,在河对岸岸边选定一个目标点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,在近岸取点B,C,D,使得ABBC,C <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> DBC,EBC上,并且点A,E,D在同一条直线上,若测得BE <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 20 m,EC=10 m,CD=20 m,则河的宽度AB等于( )

A.60 m B.40 m C.30 m D.20 m


 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

2题图 3题图

3.如图,在△ABC中,M,N分别是边AB,AC的中点,则△AMN的面积与四边形MB <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> CN的面积比为( )

A. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> B. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> C. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> D. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

4. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 值是( )

A.14 B.42 C.7 D. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

5.如图,在△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中,点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 分别是 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的中点,则下列结论:① <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ;②△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ;③ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 其中正确的有( )

A <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>
 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>
 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .3 B.2个    C.1 D.0









6.如图, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> // <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> // <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 分别交 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 于点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,则图中共有相似三角形( )

A.4B.5C. 6D.7

7.已知△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 如图所示,则下列4个三角形中,与△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 相似的是( )

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

8.如图,已知在△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ABC,DEF分别是边ABACBC上的点,DEBC,EFAB,ADDB=3∶5,那么CFCB等于( )

A.5∶8 B.3∶8

C.3∶5 D.2∶5

9.如图,笑脸盖住的点坐标可能为( )

A <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> B <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> C. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> D. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

组合 1493 组合 1732










10.如图,正五边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 是由正五边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 经过位似变换得到的,若 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

则下列结论正确的是( )

A. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> B. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> C. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> D. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

1 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 1.如果一个直角三角形的两条边长分别是68,另一个与它相似的直角三角形边长分别是3,4 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,那么 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的值( )

A.只有1

B.可以有2

C.可以有3

D.有无数个

12.如图, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 是△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的边 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 上任一点,已知 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .若△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的面积为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,则△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的面积为( )

A. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> B. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> C. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> D. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

二、填空题(每小题3分,共18分)

13.已知 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,且 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,则 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> _______.

14.如图,为估计池塘两岸边A,B两点间的距离,在池塘的一侧选取点O,分别取OAOB的中点MN,测的MN=32 m,则AB两点间的距离是___________m.

15.如图,在△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,则 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ______

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>



16.如图,在△ABC中,DEBC,  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,ADE的面积为8,则△ABC的面积为 .

17.如图,阳光从教室的窗户射入室内,窗户框 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 在地面上的影长 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,窗户下沿到地面的距离 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,那么窗户的高 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ________.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 组合 1844







18.如图,在矩形ABCD中,AD=5AB=7.EDC上一个动点,把△ADE沿AE折叠,当点D的对应点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 落在∠ABC的平分线上时,DE的长为 .

三、解答题(共78分)

19.8分)已知线段 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 成比例( <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ),且a=6 cm <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,求线段 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的长度.

20.8分)如图,梯形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 上,

连结 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 并延长与 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的延长线交于点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

1)求证:△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

2)当点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的中点时,过点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 于点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,若 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,求 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的长.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

组合 1680








21.8分)试判断如图所示的两个矩形是否相似.自选图形 1345

22.8分)已知:如图,在△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 在边 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 上, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 相交于点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,且∠ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

组合 1683
组合 1685
证:(
1)△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ;(
2 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

2312分)如图,在正方形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 分别是边 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 上的点, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 连结 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 并延长 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的延长线于点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 1)求证: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

2)若正方形的边长为4,求 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的长.

24.8分)已知:如图所示的一张矩形纸片 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

将纸片折叠一次,使点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 重合,再展开,折痕 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 边于 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,交 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 边于 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,分别连结 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

(1)求证:四边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 是菱形. h

(2)若AE=10 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的面积为24,求 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的周长.

(3)在线段 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 上是否存在一点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,使得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

若存在,请说明点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的位置,并予以证明;若不存在,请说明理由.

25.12分)如图,在 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 在边 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 上,连接 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,将线段 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 绕点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 顺时针旋 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 位置,连接 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

组合 1811 1)求证: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ;(2)若 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,求证:四边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 为正方形.









25题图

26.(14)某一天,小明和小亮来到一河边,想用遮阳帽和皮尺测量这条河的大致宽度,两人在确保无安全隐患的情况下,先在河岸边选择了一点B(B与河对岸岸边上的一棵树的底部点D所确定的直线垂直于河岸).

小明在B点面向树的方向站好,调整帽檐,使视线通过帽檐正好落在树的底部点D处,如图所示,这时小亮测得小明眼睛距地面的距离AB=1.7米;②小明站在原地转动180°后蹲下,并保持原来的观察姿态(除身体重心下移外,其他姿态均不变),这时视线通过帽檐落在了DB延长线上的点E处,此时小亮测得BE=9.6米,小明的眼睛距地面的距离CB=1.2.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

26题图


根据以上测量过程及测量数据,请你求出河宽BD是多少米?




23章 图形的相似检测题参考答案

1.D 解析:根据相似图形的定义知,A <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> BC项中的两个图形都为相似图形,D项中的两个图形一个是等边三角形,一个是直角三角形,不是相似图形.

2.B 解析:∵ ABBC,CDBC,∴ ABCD,∴ ∠A=∠D.又∠AEB=∠DEC

∴ △BAE∽△CDE,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

BE <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 20 mEC <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 10 mCD <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 20 m,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴ AB=40 m.

3.B 解析:∵ 在△ABC中,点M,N分别是边AB,AC的中点,∴ MNBCMN= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> BC,

∴ △AMN∽△ABC, ∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

4.D 解析:设 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,则 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 所以15x-14x+8x=3,x= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

5.A 解析:因为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 分别是 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的中点,所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的中位线.由中位线的性质可推出①②③全部正确.

6.C 解析:△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

7.C 解析:由 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 对照四个选项知,C项中的三角形与△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 相似.

8. A 解析:本题考查了相似三角形的判定和性 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>.∵ DEBC,∴ ∠ADE=∠B.

又∵ ∠A=∠A,∴ △ADE∽△ABC,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .∵ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> , <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

AE=3 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,A <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> C=8 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴ CE=AC-AE=5 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .∵ EFAB,∴ △CEF∽△C <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> AB,

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

9.D 解析 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>A项的点在第一象限;B项的点在第二象限;C项的点在第三象限;D项的点在第四象限.笑脸在第四象限,所以选D.

10.B 解析:由正五边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 是由正五边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 经过位似变换得到的,知 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 所以选项B正确.

11.B 解析:当一个直角三角形的两直角边长为68,且另一个与它相似的三角形的两直角边长为3,4时, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的值为5;当一个直角三角形的一直角边长为6,斜边长为8,另一直角边长为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,且另一个与它相似的直角三角形的一直角边长为3,斜边长为4时, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的值为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> . <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的值可以为5 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .(其他情况均不成立)

12.C 解析:因为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

13.4 解析:因为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

所以设 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

14.64 解析:根据三角形中位线定理,得AB=2MN=2×32=64m.

15.9 解析:在△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中,因为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,所以∠ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

所以△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

16.18 解析: DEBC,∴ ABCADE,∴ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ADE的面积为8,∴ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 解得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> =18.

17. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 解析:∵  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴ △ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> . <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

18. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 解析:如图,过点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 作直线 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 于点M,交CD于点N,连接 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

18题答图



 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 平分 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中,设 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,则 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,在 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,解得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

故当 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 时, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ;当 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 时, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

19.分析:列比例式时,单位一定要统一,做题时要看仔细.

解:∵  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 6 cm <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 解得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

20.1)证明:∵ 在梯形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

2)解: 由(1)知,△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,又 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的中点,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

∴ △ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ≌△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

又∵  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

BG=2EF <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> -AB=2×4-6=2(cm),∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

21.分析:要判定两个多边形相似,必须对应角相等,对应边成比例 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,因矩形的四个角都是直角,符合对应角相等,只要证明对应边成比例即可.

解:因为两个图形都是矩形,显然它们的四个角都分别相等.

从图中数据观察可知小矩形的长为20,宽为10

于是两个矩形的长之比为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,宽之比为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,

符合对应边成比例,对应角相等,故这两个矩形是相似的.

22.证明:(1)∵ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴ ∠ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

又∵  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

2)由 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

又∵∠ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> . ∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

23.1)证明:在正方形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

2)解:∵  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

∵ △ABE∽△DEF,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴ △ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

24.(1)证明:由题意可知OA=OCEFAC.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∠ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> =∠ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ≌△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> . <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 四边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> AFCE是平行四边形. 

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 四边形AFCE是菱形.

2解: 四边形AFCE是菱形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> a2+b2=100. ABF的面积为24,∴ ab=48

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> a+b=14a+b=-14(不合题意,舍去).

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的周长为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

(3)解:存在,过点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 的垂线,交 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 于点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 就是符合条件的点.

证明如下

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 90°,∠ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>    <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

四边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 是菱形,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> w

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

25.证明:(1)∵  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 中,

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

2)∵  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴ 四边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 是矩形.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> ,∴ 四边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> 是正方形.

26.解:由题意,知∠BAD=∠BCE.∵ ∠ABD=∠CBE=90°

∴ △BAD∽△BCE.∴  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> .∴ BD=13.6.

河宽BD13.6.

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