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【323420】2023九年级数学上册 第3章 图形的相似3.3相似的图形同步测试题(新版)湘教版

时间:2025-01-16 18:33:09 作者: 字数:4246字
简介:


33 相似的图形


1.观察如图所示的四组图形,不相似的图形是(   )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/941/" title="似的" class="c1" target="_blank">似的</a>

2.已知△DEF∽△ABC,且∠A50°,∠B40°,则∠F的度数是(   )

A50° B20°

C70° D90°

3.在△ABC中,BC13AC11AB15,另一个与它相似的三角形的最大边长为10,则它的最小边长为(   )

A. B. C. D.

4.小张用手机拍摄得到图①,经放大后得到图②.图①中的线段AB在图②中的对应线段是(   )

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AFG BFH CEH DEF

5.如果△ABC∽△ABC,且△ABC与△ABC的相似比为k1,△ABC与△ABC的相似比为k2,则k1k2的关系是(   )

Ak1k2 Bk1k20 Ck1·k2=-1 Dk1·k21

6.如图,△ABC∽△ADE,且∠ADE=∠B,则下列比例式正确的是(   )

A.B.C.D.

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7.如图,△AOB∽△DOCOA2AD9OB5DC12,∠A58°,∠AOB72°,求ABOC的长和∠C的度数.

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8.下列图形中,是相似形的是(   )

A.所有平行四边形 B.所有矩形 C.所有菱形 D.所有正方形

9.两个相似多边形的一组对应边分别为3 cm4.5 cm,那么它们的相似比为(   )

A. B. C. D.

10.如图,下列两个四边形若相似,则下列结论不正确的是(   )

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A.∠α100° Bx

CyDx7

11(易错题)在△ABC,点DE分别在ABAC上,且==2,则△ADE与△ABC的相似比为(   )

A. B2 C. D.

12.如图,Rt△ABC∽Rt△DEF,∠A35°,则∠E的度数为(   )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/941/" title="似的" class="c1" target="_blank">似的</a>

A35° B45° C55° D65°

13.如图,△ABC∽△ACD,若∠ACB80°,则∠ADC的度数为(   )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/941/" title="似的" class="c1" target="_blank">似的</a>

A30° B50° C80° D.无法确定

14.若如图所示的两个四边形相似,则∠α的度数是(   )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/941/" title="似的" class="c1" target="_blank">似的</a>

A60° B75° C87° D120°

15.如图,在▱ABCD中,AB10AD6EAD的中点,点FAB上,且△BCF∽△DCE,则BF的长是(   )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/941/" title="似的" class="c1" target="_blank">似的</a>

A8.2 B3.6 C5 D1.8

16.已知△ABC与△ABC相似,相似比为2∶3;△ABC与△ABC相似,相似比为5∶4,那么△ABC与△ABC的相似比为(   )

A5∶6 B6∶5 C15∶8 D8∶15

17.如图,有两个相似的星星图案,则x的值是(   )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/941/" title="似的" class="c1" target="_blank">似的</a>

A15 B12 C10 D8

18.如图,△ADE∽△ABC,若AD1AB3,则△ADE与△ABC的相似比是_________

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19.矩形ABCD与矩形ABCD中,AB40BC20AB20BC10,则矩形ABCD与矩形ABCD′_______相似.(填“一定”或“不一定”)

20.如图,已知△ABC∽△ADEAE5 cmEC3 cmBC7 cm,∠BAC45°,∠C40°.

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(1)求∠AED和∠ADE的大小;

(2)DE的长.



21.如图,已知四边形ABCD四边形ABCD,求∠A的度数及x的值.

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22.在一矩形ABCD的花坛四周修筑小路,使得相对两条小路的宽均相等,如果花坛AB20米,AD30米,问小路的宽xy的比值为多少时,能使得小路四周所围成的矩形ABCD与矩形ABCD相似?请说明理由.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/50/" title="同步" class="c1" target="_blank">同步</a> <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/941/" title="似的" class="c1" target="_blank">似的</a>






答案:

1---6 CDADDD

7. 解:根据题意有:ODADOA7,==,∴==,∴==,∴OC17.5AB=,∠CB180°A-∠AOB50° 

8----17 DADDC CCDAD

18. 1:3


19. 一定

20. 解:(1)AED40°,∠ADE95°

(2)∵△ABC∽△ADE,∴=,即=,∴DE4.375 cm 

21. 解:四边形ABCD∽四边形A′B′C′D′,∴∠A=∠A,=.∵∠A′107°AB5AD4AB2,∴∠A107°,=,∴x= 

22. 解:由题意知20∶(202y)30∶(302x),∴3y2x,即=,即=时,矩形A′B′C′D′与矩形ABCD相似






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