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【323421】2023九年级数学上册 第3章 图形的相似3.4.1 相似三角形的判定练习(新版)湘教

时间:2025-01-16 18:33:14 作者: 字数:22746字
简介:


3.4.1 相似三角形的判定》

 

一、填空题

1  三角形一边的  和其他两边  ,所构成的三角形与原三角形相似.

2.如果两个三角形的  对应边的  ,那么这两个三角形相似.

3.如果两个三角形的  对应边的比相等,并且  相等,那么这两个三角形相似.

4.如果一个三角形的  角与另一个三角形的  ,那么这两个三角形相似.

5.在ABCA′B′C′中,如果A=56°B=28°A′=56°C′=28°,那么这两个三角形能否相似的结论是  ,理由是  

6.在ABCA′B′C′中,如果A=48°C=102°A′=48°B′=30°,那么这两个三角形能否相似的结论是  ,理由是  

7.在ABCA′B′C′中,如果A=34°AC=5cmAB=4cmA′=34°A′C′=2cmA′B′=1.6cm,那么这两个三角形能否相似的结论是  ,理由是  

8.在ABCDEF中,如果AB=4BC=3AC=6DE=2.4EF=1.2FD=1.6.那么这两个三角形能否相似的结论是  ,理由是  

9.如图,ABC的两条高ADBE交于点H,则图中的相似三角形共有  对.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

10.如图所示,▱ABCD中,GBC延长线上的一点,AGBD交于点E,与DC交于点F,此图中的相似三角形共有  对.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 

二、选择题

11.如图,不能判定ABC∽△DAC的条件是(  ) <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AB=DAC BBAC=ADC CAC2=DC•BC DAD2=BD•BC

12.如图,在平行四边形ABCD中,AB=10AD=6EAD的中点,在AB上取一点F,使CBF∽△CDE,则BF的长是(  )

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A5 B8.2 C6.4 D1.8

13.如图所示,小正方形的边长均为1,则下列选项中阴影部分的三角形与ABC相似的是(  )

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 

三、解答题

14.如图,在RtABC中,ACB=90°CDABD

1)图中有哪两个三角形相似?

2)求证:AC2=AD•ABBC2=BD•BACD2=AD•BD

3)若AD=2DB=8,求ACBCCD的长;

4)若AC=6DB=9,求ADCDBC的长;

5)求证:AC•BC=AB•CD

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

15.如图所示,如果DEF分别在OAOBOC上,且DFACEFBC.求证:

1ODOA=OEOB

2ODE∽△OAB

3ABC∽△DEF

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

16.如图,已知ABCDADBC相交于EFEC上一点,且EAF=C

求证:(1EAF=B;(2AF2=FE•FB

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

17.已知:如图,在梯形ABCD中,ABCDB=90°,以AD为直径的半圆与BC相切于E点.求证:AB•CD=BE•EC

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

18.如图,ABO的直径,BCO的切线,切点为点B,点DO上的一点,且ADOC.求证:AD•BC=OB•BD

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

19.已知:如图,在O中,CD过圆心O,且CDAB,垂足为D,过点C任作一弦CFOF,交ABE.求证:CB2=CF•CE

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

20.已知DBC边延长线上的一点,BC=3CDDFAC边于E点,且AE=2EC,试求AFFB的比.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

21.已知:如图,在ABC中,BAC=90°AHBCH,以ABAC为边在RtABC外作等边ABDACE,试判断BDHAEH是否相似,并说明理由.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

22.如图,在ABC中,C=90°PAB上一点,且点P不与点A重合,过点PPEABAC边于E点,点E不与点C重合,若AB=10AC=8,设AP的长为x,四边形PECB的周长为y,求yx之间的函数关系式.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 

3.4.1 相似三角形的判定》


参考答案与试题解析

 

一、填空题

1 平行于 三角形一边的 直线 和其他两边 相交 ,所构成的三角形与原三角形相似.

【考点】相似三角形的判定.

【分析】平行于三角形一边的直线和其他两边(或两边的延长线)相交,所得的三角形与原三角形的三边对应成比例.所以所构成的三角形与原三角形相似.

【解答】解:平行于三角形一边的 直线和其他两边 相交,所构成的三角形与原三角形相似.

故答案是:平行于;直线;相交.

【点评】本题考查了相似三角形的判定.(1)平行线法:平行于三角形的一边的直线与其他两边相交,所构成的三角形与原三角形相似;

2)三边法:三组对应边的比相等的两个三角形相似;

3)两边及其夹角法:两组对应边的比相等且夹角对应相等的两个三角形相似;

4)两角法:有两组角对应相等的两个三角形相似.

 

2.如果两个三角形的 三组 对应边的 比相等 ,那么这两个三角形相似.

【考点】相似三角形的判定.

【分析】由三边法:三组对应边的比相等的两个三角形相似;即可求得答案.

【解答】解:如果两个三角形的三组对应边的比相等,那么这两个三角形相似.

故答案为:三组,比相等.

【点评】此题考查了相似三角形的判定.注意熟记相似三角形的判定定理是关键.

 

3.如果两个三角形的 两组 对应边的比相等,并且 夹角对应 相等,那么这两个三角形相似.

【考点】相似三角形的判定.

【分析】由两边及其夹角法:两组对应边的比相等且夹角对应相等的两个三角形相似;即可求得答案.

【解答】解:如果两个三角形的两组对应边的比相等,并且夹角对应相等,那么这两个三角形相似.

故答案为:两组,夹角对应.

【点评】此题考查了相似三角形的判定.注意熟记相似三角形的判定定理是关键.

 

4.如果一个三角形的 两个 角与另一个三角形的 两个角对应相等 ,那么这两个三角形相似.

【考点】相似三角形的判定.

【分析】根据“两角法”来判定两个三角形相似.

【解答】解:如果一个三角形的两个角与另一个三角形的两个角对应相等,那么这两个三角形相似.

故答案为:两个,两个角对应相等.

【点评】本题考查了相似三角形的判定.两角法:有两组角对应相等的两个三角形相似.

 

5.在ABCA′B′C′中,如果A=56°B=28°A′=56°C′=28°,那么这两个三角形能否相似的结论是 ABC∽△A′C′B′ ,理由是 有两组角对应相等的两个三角形相似 

【考点】相似三角形的判定.

【分析】由已知条件易得A=A′B=C′,则根据有两组角对应相等的两个三角形相似可判断两三角形相似.

【解答】解:∵∠A=56°B=28°A′=56°C′=28°

∴∠A=A′B=C′

∴△ABC∽△A′C′B′

故答案为ABC∽△A′C′B′;有两组角对应相等的两个三角形相似.

【点评】本题考查了相似三角形的判定:有两组角对应相等的两个三角形相似.

 

6.在ABCA′B′C′中,如果A=48°C=102°A′=48°B′=30°,那么这两个三角形能否相似的结论是 ABC∽△A′B′C′ ,理由是 有两组角对应相等的两个三角形相似 

【考点】相似三角形的判定.

【专题】常规题型.

【分析】先根据三角形内角和定理计算出B=30°,于是得到A=A′B=B′,所以根据有两组角对应相等的两个三角形相似可证明∴△ABC∽△A′B′C′

【解答】解:∵∠A=48°C=102°

∴∠B=180°﹣A﹣C=30°

A′=48°B′=30°

∴∠A=A′B=B′

∴△ABC∽△A′B′C′

故答案为ABC∽△A′B′C′;有两组角对应相等的两个三角形相似.

【点评】本题考查了相似三角形的判定:有两组角对应相等的两个三角形相似.

 

7.在ABCA′B′C′中,如果A=34°AC=5cmAB=4cmA′=34°A′C′=2cmA′B′=1.6cm,那么这两个三角形能否相似的结论是 ABC∽△A′B′C′ ,理由是 两组对应边的比相等且夹角对应相等的两个三角形相似 

【考点】相似三角形的判定.

【专题】常规题型.

【分析】先计算出 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,得到 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,加上A=A′=34°,于是根据两组对应边的比相等且夹角对应相等的两个三角形相似可判断两三角形相似.

【解答】解:AC=5cmAB=4cmA′C′=2cmA′B′=1.6cm

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A=A′=34°

∴△ABC∽△A′B′C′

故答案为ABC∽△A′B′C′;两组对应边的比相等且夹角对应相等的两个三角形相似.

【点评】本题考查了相似三角形的判定:两组对应边的比相等且夹角对应相等的两个三角形相似.

 

8.在ABCDEF中,如果AB=4BC=3AC=6DE=2.4EF=1.2FD=1.6.那么这两个三角形能否相似的结论是 ABC∽△DEF ,理由是 三组对应边的比相等的两个三角形相似 

【考点】相似三角形的判定.

【分析】先求出两三角形对应边的比,进而可得出结论.

【解答】解: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

∴△ABC∽△DEF

故答案为:ABC∽△DEF,三组对应边的比相等的两个三角形相似.

【点评】本题考查的是相似三角形的判定定理,熟知三组对应边的比相等的两个三角形相似是解答此题的关键.

 

9.如图,ABC的两条高ADBE交于点H,则图中的相似三角形共有 6 对.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】相似三角形的判定.

【分析】根据相似三角形的判定定理进行解答即可.

【解答】解:ADBCBEAC

∴∠ADC=ADB=AEB=BED=90°

∴△AEH∽△ADC∽△BDH∽△BEC

共有6对相似三角形.

故答案为:6

【点评】本题考查的是相似三角形的判定定理,熟知有两组角对应相等的两个三角形相似是解答此题的关键.

 

10.如图所示,▱ABCD中,GBC延长线上的一点,AGBD交于点E,与DC交于点F,此图中的相似三角形共有 6 对.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】相似三角形的判定;平行四边形的性质.

【分析】根据平行四边形的对边平行,再根据平行于三角形一边的直线和其他两边(或两边的延长线)相交,所构成的三角形与原三角形相似找出相似三角形即可得解.

【解答】解:在▱ABCD中,

ABCD

∴△ABE∽△FDEABG∽△FCG

ADBC

∴△ADE∽△GBEFDA∽△FCG

∴△ABG∽△FDAABD∽△BCD

图中相似三角形有6对.

故答案为:6

【点评】本题考查了相似三角形的判定,主要利用了平行于三角形一边的直线和其他两边(或两边的延长线)相交,所构成的三角形与原三角形相似,要注意ABGFDA都与FCG相似,所以也相似,这也是本题容易出错的地方.

 

二、选择题

11.如图,不能判定ABC∽△DAC的条件是(  ) <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AB=DAC BBAC=ADC CAC2=DC•BC DAD2=BD•BC

【考点】相似三角形的判定.

【专题】常规题型.

【分析】已知有公共角C,则AB选项可根据有两组角对应相等的两个三角形相似来判定;C选项可以根据两组对应边的比相等且相应的夹角相等的两个三角形相似来判定;D选项虽然也是对应边成比例但无法得到其夹角相等,所以不能推出两三角形相似.

【解答】解:已知ABCDCA中,ACD=BAC;如果ABC∽△DAC,需满足的条件有:

DAC=BADC=BAC

AC2=DC•BC

故选D

【点评】此题主要考查学生对相似三角形判定方法的运用.

 

12.如图,在平行四边形ABCD中,AB=10AD=6EAD的中点,在AB上取一点F,使CBF∽△CDE,则BF的长是(  )

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A5 B8.2 C6.4 D1.8

【考点】相似三角形的性质;平行四边形的性质.

【专题】压轴题.

【分析】由CBF∽△CDE,根据相似三角形的对应边对应成比例,可知BFDE=BCDC,即BF=BCDC×DE.又四边形ABCD是平行四边形,根据平行四边形的对边相等,可知BC=AD=6DC=AD=10,易知DE=3,从而求出BF的长.

【解答】解:在平行四边形ABCD中,AB=10AD=6EAD的中点,

CD=10BC=6DE=3

∵△CBF∽△CDE

BFDE=BCDC

BF=6÷10×3=1.8

故选D

【点评】本题主要考查了平行四边形的性质及相似三角形的性质:平行四边形的对边相等.相似三角形的对应边成比例.

 

13.如图所示,小正方形的边长均为1,则下列选项中阴影部分的三角形与ABC相似的是(  )

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】相似三角形的判定.

【分析】根据网格中的数据求出ABACBC的长,求出三边之比,利用三边对应成比例的两三角形相似判断即可.

【解答】解:根据题意得:AB= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> AC=2BC= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

BCACAB=1 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A、三边之比为1 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,图中的三角形(阴影部分)与ABC相似;

B、三边之比 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>2 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 3,图中的三角形(阴影部分)与ABC不相似;

C、三边之比为1 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>2 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,图中的三角形(阴影部分)与ABC相似;

D、三边之比为2 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,图中的三角形(阴影部分)与ABC不相似.

故选A

【点评】此题考查了相似三角形的判定,熟练掌握相似三角形的判定方法是解本题的关键.

 

三、解答题

14.如图,在RtABC中,ACB=90°CDABD

1)图中有哪两个三角形相似?

2)求证:AC2=AD•ABBC2=BD•BACD2=AD•BD

3)若AD=2DB=8,求ACBCCD的长;

4)若AC=6DB=9,求ADCDBC的长;

5)求证:AC•BC=AB•CD

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】相似三角形的判定与性质.

【分析】(1)由条件可知A=DCBACD=B,可证得ACD∽△ABC∽△CDB

2)利用(1)可得到 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,可证得结论;

3)代入(2)中结论可求得;

4)同(3)代入(2)可求得;

5)利用面积相等即可得出结论.

【解答】(1)解:∵∠ACB=90°CDAB

∴∠ADC=ACB

∴∠ACD+∠A=A+∠B=90°

∴∠ACD=B

∴△ACD∽△ABCACD∽△CDB

同理可证得CDB∽△ABC

相似的三角形有:ACDABCACDCDBCDBABC

2)证明:∵△ACD∽△ABC

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AC2=AD•AB

同理可得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

BC2=BD•ABCD2=AD•BD

3)解:AD=2DB=8

CD2=AD•BD=2×8=16

CD=4

AB=AD+BD=10

AC2=AD•AB=2×10=20BC2=BD•AB=8×10=80

AC=2 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> BC=4 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

4)解:AC=6DB=9,且AB=AD+BD

AC2=ADAD+BD),即62=AD2+9AD

解得AD=3或(﹣12舍去),

CD2=AD•BD=3×9=27

CD=3 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AB=AD+BD=12

BC2=BD•AB=9×12=108

BC=6 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

5)证明:SABC= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> AC•BC,且SABC= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> CD•AB

AC•BC=CD•AB

【点评】本题主要考查相似三角形的判定和性质,掌握直角三角形中角之间的关系是解题的关键,注意方程思想的应用.

 

15.如图所示,如果DEF分别在OAOBOC上,且DFACEFBC.求证:

1ODOA=OEOB

2ODE∽△OAB

3ABC∽△DEF

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】相似三角形的判定与性质.

【专题】证明题.

【分析】(1)根据平行于三角形一边的直线截其他两边所得的新三角形与原三角形相似就可以得出结论;

2)根据ODOA=OEOBAOB=AOB就可以得出ODE∽△OAB

3)由ODE∽△OAB就可以得出 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 就可以得出结论.

【解答】证明:(1DFACEFBC

∴△ODF∽△OACOEF∽△OBC

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

ODOA=OEOB

2ODOA=OEOBDOE=AOB

∴△ODE∽△OAB

3∵△ODE∽△OAB

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

∴△ABC∽△DEF

【点评】本题考查了平行于三角形一边的直线截其他两边所得的新三角形与原三角形相似的判定方法的运用,相似三角形的性质的运用,相似三角形的判定的运用,解答时证明三角形相似是关键.

 

16.如图,已知ABCDADBC相交于EFEC上一点,且EAF=C

求证:(1EAF=B;(2AF2=FE•FB

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】相似三角形的判定与性质;平行线的性质.

【专题】证明题.

【分析】(1)欲证EAF=B,通过ABCD及已知发现它们都与C相等,等量转换即可;

2)欲证AF2=FE•FB,可证AFB∽△EFA得出.

【解答】证明:(1ABCD

∴∠B=C

∵∠EAF=C

∴∠EAF=B


2)在AFBEFA中,

∵∠EAF=BAFB=EFA

∴△AFB∽△EFA

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AF2=FE•FB

【点评】乘积的形式通常可以转化为比例的形式,由相似三角形的性质得出,同时考查了平行线的性质.

 

17.已知:如图,在梯形ABCD中,ABCDB=90°,以AD为直径的半圆与BC相切于E点.求证:AB•CD=BE•EC

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】相似三角形的判定与性质;梯形;切线的性质.

【专题】证明题.

【分析】连结AEED,由平行线的性质推出B=C,由AD为直径,得出AED=90°,从而证得AEB=CDE=90°﹣DEC,根据相似三角形的判定证得ABE∽△ECD,由相似三角形的性质即可证得结论.

【解答】解:连结AEED

ABCDB=90°

∴∠C=90°

∴∠B=C

AD为直径,

∴∠AED=90°

AEB=CDE=90°﹣DEC

∴△ABE∽△ECD

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AB•CD=BE•EC

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【点评】本题主要考查了直径所对的圆周角的性质,相似三角形的判定和性质,能证得AEB=CDE是解题的关键.

 

18.如图,ABO的直径,BCO的切线,切点为点B,点DO上的一点,且ADOC.求证:AD•BC=OB•BD

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】切线的性质;圆周角定理;相似三角形的判定与性质.

【专题】证明题.

【分析】要证AD•BC=OB•BD,即要证ADOB=BDBC,于是求证ABD∽△OCB即可.

【解答】证明:BCO的切线,AB是圆的直径,

∴∠CBO=D=90°

ADOC

∴∠COB=A

∴△ABD∽△OCB

ADOB=BDBC

AD•BC=OB•BD

【点评】本题利用了相似三角形的判定和性质求解.

 

19.已知:如图,在O中,CD过圆心O,且CDAB,垂足为D,过点C任作一弦CFOF,交ABE.求证:CB2=CF•CE

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】垂径定理;相似三角形的判定与性质.

【专题】证明题.

【分析】连接BF,证所求的对应边成比例线段所在的三角形相似即可,即证CBE∽△CFB

【解答】证明:连接FB,(1分)

CD过圆心O,且CDAB

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .(2分)

∴∠CBE=F

∵∠BCE为公共角,

∴△CBE∽△CFB.(4分)

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .(5分)

CB2=CE•CF.(6分)

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【点评】此题考查了垂径定理及相似三角形的判定和性质.

 

20.已知DBC边延长线上的一点,BC=3CDDFAC边于E点,且AE=2EC,试求AFFB的比.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】平行线分线段成比例.

【分析】过CCGABDFG,于是得到CDG∽△BDFCEG∽△AFE,根据相似三角形的性质得到 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,求得BF=4CGAF=2CG,即可得到结论.

【解答】解:过CCGABDFG

∴△CDG∽△BDFCEG∽△AFE

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

BC=3CD

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

BF=4CG

AE=2EC

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AF=2CG

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【点评】本题考查了相似三角形的判定和性质熟练掌握相似三角形的判定和性质是解题的关键.

 

21.已知:如图,在ABC中,BAC=90°AHBCH,以ABAC为边在RtABC外作等边ABDACE,试判断BDHAEH是否相似,并说明理由.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】相似三角形的判定;等边三角形的性质.

【分析】首先由在ABC中,BAC=90°AHBCH,证得BHA∽△AHC,即可得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,又由以ABAC为边在RtABC外作等边ABDACE,可得 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> HBD=HAE,则可证得BDH∽△AEH

【解答】解:相似.

理由:ABC中,BAC=90°

∴∠BAH+∠CAH=90°

AHBC

∴∠AHB=CHA=90°

∴∠ABH+∠BAH=90°

∴∠BAH=CAH

∴△BAH∽△ACH

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

∵△ABDACE是等边三角形,

BA=BDAC=AEABD=CAE=60°

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> HBD=HAE

∴△BDH∽△AEH

【点评】此题考查了相似三角形的判定与性质以及直角三角形的性质.注意证得BAH∽△ACH是关键.

 

22.如图,在ABC中,C=90°PAB上一点,且点P不与点A重合,过点PPEABAC边于E点,点E不与点C重合,若AB=10AC=8,设AP的长为x,四边形PECB的周长为y,求yx之间的函数关系式.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【考点】相似三角形的判定与性质;根据实际问题列一次函数关系式;勾股定理.

【专题】代数几何综合题;数形结合.

【分析】四边形PECB的周长为PE+EC+CB+BP,其中BC在直角ABC中运用勾股定理可以求出,BP=AB﹣AP=10﹣x,另外两条边均可根据AEP∽△ABC,借助于比例线段,用含有x的式子表示出来.关键还需求出自变量x的取值范围,这可以令E点运行到C时,求特殊值.

【解答】解:ABC中,C=90°AB=10AC=8

BC=6

EPABA为公共角,

∴△AEP∽△ABC

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AP=x

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AE= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> PE= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

EC重合时,CPAB

∴△APC∽△ACB

CA2=AP•AB

82=10AP

AP= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

因为PA不重合,EC不重合,

所以 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

【点评】本题实际还是考查相似三角形的判定以及一次函数在几何图形中的应用.

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