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【330715】第一章 三角形的证明 周周测3(1.2)

时间:2025-02-11 18:39:18 作者: 字数:9158字

 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

1.2直角三角形

一、选择题

1.要判定两个直角三角形全等,下列说法正确的有(  

有两条直角边对应相等;
有两个锐角对应相等;
有斜边和一条直角边对应相等;
有一条直角边和一个锐角相等;
有斜边和一个锐角对应相等; 
有两条边相等.

A. 6                               B. 5                                     C. 4                                       D. 3

2.已知直角三角形中30°角所对的直角边为2cm,则斜边的长为( 

A. 2cm                                     B. 4cm                                     C. 6cm                                  D. 8cm

3.在下列条件中不能判断两个直角三角形全等的是(  )

A. 已知两个锐角      <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. 已知一条直角边和一个锐角     

 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. 已知两条直角边      <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. 已知一条直角边和斜边

4.把直线a沿箭头方向平移1.5cm得直线b,这两条直线之间的距离是(   
 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A. 1.5cm                                 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. 3cm                                 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. 0.75cm                            <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D.  <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> cm

5.如图,在ABC中,B30°ED垂直平分BCED3.则CE长为(   

 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A. 6                                            <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. 9                                            <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. 3                                      <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. 8

6.如图,RtABC中,C90°B30°AB的垂直平分线DEAB于点D,交BC于点E,则下列结论不正确的是( )
 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A. AEBE                        <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. ACBE                      <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. CEDE                   <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. CAEB

7.如图,RtABC中,B=90°ACB=60°,延长BCD,使CD=AC。则ACBD=  
 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A. 11                                     <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. 31                                <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. 41                                     <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. 23

8.如图,ABC中,C=90°AB=6B=30°,点PBC边上的动点,AP的长不可能是( 
 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A. 2.5                                <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. 4.2                                        <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. 5.8                                        <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. 3.6

9.如图,在梯形ABCD中,ABCDA=60°B=30°,若AD=CD=6,则AB的长等于(       )
 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A. 9                                       B. 12                               C.  <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>                                        D. 18

10.ABC,ACB=90°,A=30°,CDABD,AB=4,BD的长为(    .

A. 3                                            <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. 4                                            <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. 1                                     <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. 7

二、填空题

11.已知AB=20AC=30A=150°,则ABC的面积是________

12.如图,BCACDEACAD=BDA=30°DE=3.6,则AB=________

 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

三、解答题

13.如图,在ABC中,AD=BDADBC于点DC=55°,求BAC的度数.
 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>





14.如图所示,ABBCDCAC,垂足分别为BC,过D点作BC的垂线交BCF,交ACEAB=EC,试判断ACED的长度有什么关系并说明理由.

 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>








15.已知:如图,ABCDDEACBFACEF是垂足,DE=BF
 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  

1)求证: AF=CE

2)求证:ABCD












参考答案

1.B 2.B 3.A 4.C 5.A 6.B 7.D 8.A 9.D 10.C

11.150 12.14.4

13.解:∵AD⊥BC
∴∠ADB=∠ADC=90°
∵∠C=55°
∴∠CAD=90°-∠C=90°-55°=35°
∵AD=BD
∴∠BAD=∠B=45°
∴∠BAC=∠BAD+∠DAC=45°+35°=80°


14.解:AC=ED,理由如下:
∵AB⊥BCDC⊥ACED⊥BC
∴∠B=∠EFC=∠DCE=90°
∴∠A+∠ACB=90°,∠CEF+∠ACB=90°
∴∠A=∠CEF

 <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/886/" title="证明" class="c1" target="_blank">证明</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

∴△ABC≌△ECDASA).
∴AC=ED(全等三角形的对应边相等).


15.证明:(1)∵DE⊥ACBF⊥AC
Rt△DCERt△BAF中,
AB=CDDE=BF
∴Rt△DCE≌Rt△BAFHL),
∴AF=CE
2)由(1)中Rt△DCE≌Rt△BAF
可得∠C=∠A
∴AB∥CD