当前位置:首页 > 九年级 > 数学试卷

【323485】2023九年级数学上册 第四章 图形的相似(相似三角形的判定)讲义(新版)北师大版

时间:2025-01-16 18:37:47 作者: 字数:2274字
简介:


相似三角形的判定

重难点易错点解析

判断三角形是否相似,要注意思维的完整性.

题一

题面:如图所示,△ABC的高ADBE交于点F,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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>




金题精讲

题一

题面:如图,在Rt△ABC中,∠ACB=90°CDABD,想一想,

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

(1)求证:AC2=AD·ABBC2=BD·BA

(2)求证:CD2=AD·AD

(3)求证:AC·BC=AB·CD



三角形相似





题二

题面:如图,在梯形ABCD中,ABCD,∠B=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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>



圆周角定理、相似三角形





满分 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 冲刺

题一

题面:如下图甲所示,在矩形ABCD中,AB=2AD.如图乙 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 所示,线段EF=10,在EF上取一点M,分别以EMMF为一边作矩形EMNH、矩形MFG <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> N,使矩形MFGN矩形ABCD,设MN=x,当x为何值时,矩形EMNH的面积S有最大值?最大值是多少?

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>


相似多边形、二次函数





题二

题面:已知D <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" 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边延长线上的一点 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" 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=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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>



利用平行 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 线构造相似三角形





题三

题面:如图 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 132 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>P是边长 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" 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的正方形ABCD内一点,PB=3BFBP于点B,试在射线BF上找一点M,使得以点BMC为顶 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 点的三角形与△ABP相似,作图并指出相似比k的值.

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

132



 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 相似三角形的判定































讲义参考答案

重难点易错点解析

题一 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

答案:6对.

金题精讲

题一

答案:利用三角形相似证明.

题二

答案:提示:连结AEED,证△ABE∽△ECD

满分冲刺

题一

答案: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 时,S的最大值为 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

题二

答案: <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

题三

答案:如图133

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

133

ABBCPBBF

∴∠ABP=∠CBF

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,即 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>BM1=3时,△CBM1∽△ABP.相似比k=1

 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" 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/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 时,△CBM2∽△PBA.相似比 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

BM=3 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 时,以点BMC为顶点的三角形与△ABP相似,相似比分别为1 <a href="/tags/42/" title="图形" class="c1" target="_blank">图形</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/825/" title="讲义" class="c1" target="_blank">讲义</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>


www.ishijuan.cn 爱试卷为中小学老师学生提供免费的试卷下载关注”试卷家“微信公众号免费下载试卷