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【323422】2023九年级数学上册 第3章 图形的相似试题(新版)湘教版

时间:2025-01-16 18:33:23 作者: 字数:4499字
简介:


第三章图形的相似试卷

一、填空题(每小题3,24分)

1.如果四条线段m, n, x, y成比例,m=2 , n=8 , y=20 .则线段x的长是__________.

2.边长为12cm的等边三角形按2:1的比例缩小后的三角形是边长为_________三角形.

3.已知△ABC∽△DEF, AB6 , DE 8 ,  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> ________.

4.已知三个数 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> ,请你再添一个数,写出一个比例式________.

5 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> .P是△ABCAB边上的一点,过点P作直线 (不与直线AB重合)截△ABC,使截得三角形与△ABC相似,满足这样条件的直线最多________.

6.电视节目主持人在主持节目时,站在舞台上的黄金分割点处最

自然得体,若舞台AB长为20cm,试计算主持人应走到离A

至少____________________m.(结果精确到0.1m)

7.一个4米高的电线杆的影长是6,它临近的一个建筑物的影长是36.则这个建筑的高度是_________.

8.如图,DE∥BC,FD∥AB,AD∶AC2∶3 ,AB9,BC6,则四边形BEDF的周长为_____.

二、选择题(每小题4,40分)

1.若果 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> ,则下列比例式中不正确的是( )

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

2.已知:如图2,在△ABC,∠ADE=∠C,则下列等式成立的是( )

A. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> B. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>

C. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> D. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>

3.已知正五边形ABCDE与正五边形 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 的面积比为1:2,则它们的相似比为( )

A <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> . 1:2 B. 2:1 C. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> D. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>


4.如图,两个位似图形△ABO和△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> ,若OA: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 3:1,则正确的是( )

A.AB: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 3:1 B. <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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> AB: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>

C.OA: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> =2:1 D.∠A=∠ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>

5.在比例尺是1:3800的南京交通游览图上,玄武湖隧道长约7cm,它的实际长度约为( )

A.0.266km B.2.66km C.26.6km D.266000km

6 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> .下列判断正确的是( )

A.不全等的三角形一定不是相似三角形

B.不相似的三角形一定不是全等三角形

C.相似三角形一定不是全等三角形

D.全等三角形不一定是相似三角形

7.如图, DEAB的三等分点, DF∥EG∥BC , 图中三部分的面积分别为S1,S2,S 3,

S1:S2:S3( )

A.1:2:3 B.1:2:4 C.1:3:5 D.2:3:4

8.在同一时刻的阳光下,小明的影子比小强的影子长,那么在同一路灯下( )

A.小明的影子比小强的影子长 B.小明的影子比小强的影子短

C.小明的影子和小强的影子一样长 D.无法判断谁的影子长

9.把△ABC的各边都扩大为原来的2倍,得到△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> ,下面结论不正确的是( )

A <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> .△ABC∽△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>

B.△ABC和△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 的各边、各角对应相等

C.△ABC和△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 的相似比为1:2

D.△ABC和△ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 的相似比为1:3

10.如图,四边形ABCD是平行四边形,则图中与DEF相似的三角形共有( )

A.1B.2C.3D.4




三、解答题(每题8,24分)

1. 如图,在△ABC,∠C=90°,DE⊥ABE,DF⊥BCF.求证: △DEH~△BCA

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>






2.如图,四边形AEFDEBCF是相似的梯形,AE:EB2:3,EF12 cm,ADBC的长.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>






3.如图, 平行四边形ABCD,EDC中点, AE并延长与BC延长线交于点F,

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 10 , 求四边形ABCE的面积.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>









.(12)

已知如图,平行四边形ABCD,AE:EB1:2 .

(1)AE:DC的值.

( <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 2)△AEF与△CDF相似吗?若相似,请说明理由,并求出相似比.

(3)如果 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 6cm2, <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>






















数学九年级第三章图形相似试题的答案

1526cm,等边,39164、略,54、,67.6m724m814

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 、选择题:CCCAA BCDDB

三、解答题

证明:∵DE⊥AB,DF⊥BC,∴∠D+∠DHE=∠B+∠BHF=90°

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> 而∠BHF=∠DHE ∴∠D=∠B,又∵∠HFB=∠C=90°

DEH∽△BCA

解:∵四边形AEFD∽四边形EBCF

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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> ,∴AD=8,BC=18

解:∵四边形ABCD为平行四边形

EC∥AB,DC=AB,EDC中点,

EC= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> DC= <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> AB,∵EC∥AB,有∠ECF=∠ABF,∠F=∠F,△ECF∽△ABF  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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>

.提高题

解:① ∵  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> ,∴DC=AB  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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>

相似,∵ <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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> ,DC∥AB,∴∠DCF=∠EAF,∠FDC=∠EFA ∴△AEF∽△CDF,

相似比为: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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>

③∵△AEF∽△CDF  <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</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/42/" title="图形" class="c1" target="_blank">图形</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>

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