相似三角形知识点归纳_探索三角形相似的条件
数学在中考中占据着120分的分值，且难度系数值比较大，令不少同学望而生畏，其中，更有不少知识专题模块都是中考的必考模块，例如相似三角形，这部分很容易把人给绕晕，下面河南省中招考试报名平台给大家介绍几种常见的相似题型，其把相似部分的知识点涵盖的都是比较全面的，更有一些相关解题技巧贡献给各位同学。（2017年河南省中专学校报名）ntent id=js_content style=margin: 0px; padding: 0px; overflow: hidden; color: rgb(62, 62, 62); position: relative; min-height: 350px; font-family: 'hiragino sans gb', 'microsoft yahei', arial, sans-serif; font-size: 16px; line-height: 25.6px;>portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>一、相似常见类型
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>1、a型（仿a型）相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>①a型相似 ②仿a型相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知:三角形abc中，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>de // bc。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△ade~△abc
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知:在三角形abc中，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>∠ade= ∠c。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△ade~△acb
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; border: 0px;>2、8型（仿8型）相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>①8型相似 ②仿8型相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知：ab // cd
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△abe~△dce
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知： ∠a =∠c。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△abe~△cde
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>3、k型相似portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知∠bportant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>=∠adeportant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>=∠cportant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>=90º
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';> 则：△abd~△dce
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知：∠b=∠ace=∠d
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△abc~△cde
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; border: 0px;>4、子母型相似portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>二、相似常见结论
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>1
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>若de//ab，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则dg/af=ge/bf
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>2
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>若ad平分∠bac，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则ab/ac=bd/cd
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>3
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>若四边形abcd是平行四边形，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则ae?2;=ef·fg
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>4
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>若∠dac=∠dbc，则△ade~△bce ,
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';> 可推导出△aeb~△dec
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>即上下相似可得左右相似（2017年河南省中专学校报名）
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>同理，左右相似可得上下相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; border: 0px;>三、相似三角形常见解题技巧
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>1、三角形叉叉图（即三角形内部画一把叉）
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>此类题目常常考察求线段比例或者线段长度。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>图中四对线段比ae/ed、af/bf、cd/bd、ce/ef，知二求二。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>常用辅助线做法：过点作三角形边的平行线
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>遵循原则：所做辅助线不能破坏原有线段比例
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>2、三角形的可解性
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>在一个三角形中，必然存在三角、三边、三高、周长、面积这十一个量，若已知其中任意三个不全为角的条件，则可求出其他八个条件（简称portant; word-wrap: break-word !important; border: 0px;>知三求八）。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>常见辅助线做法：作三角形边上的高
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>遵循原则：
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>①特殊角原则，即作高时常常把特殊角放在直角三角形中进行求解
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>②最长边原则，即作高时常常选择作最长边上的高，使得高在内部（2017年河南省中专学校报名）
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>③偶数边原则，即常常将偶数边作为直角三角形的斜边，方便计算
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>3、线段长度求法
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>①计算比：直接计算线段长度
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>做法：利用可解性直接求出所求比例线段的数值
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>②共线比：所求比例的两条线段在同一条直线上
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>做法：利用三角形叉叉图，构造平行线求解
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>③共三角形比：所求比例的两条线段在同一三角形中
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>做法：寻找或者构造与之相似且知内比的三角形进行求解
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>④相似比：所求比例的两条线段在两个相似三角形中（2017年河南省中专学校报名）
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>做法：找到两条线段所在的两个相似三角形，利用相似比求解
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portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>1、a型（仿a型）相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>①a型相似 ②仿a型相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知:三角形abc中，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>de // bc。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△ade~△abc
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知:在三角形abc中，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>∠ade= ∠c。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△ade~△acb
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; border: 0px;>2、8型（仿8型）相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>①8型相似 ②仿8型相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知：ab // cd
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△abe~△dce
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知： ∠a =∠c。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△abe~△cde
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>3、k型相似portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知∠bportant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>=∠adeportant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>=∠cportant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>=90º
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';> 则：△abd~△dce
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>已知：∠b=∠ace=∠d
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则：△abc~△cde
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; border: 0px;>4、子母型相似portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>二、相似常见结论
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>1
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>若de//ab，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则dg/af=ge/bf
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>2
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>若ad平分∠bac，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则ab/ac=bd/cd
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>3
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>若四边形abcd是平行四边形，
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>则ae?2;=ef·fg
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>4
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>若∠dac=∠dbc，则△ade~△bce ,
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';> 可推导出△aeb~△dec
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>即上下相似可得左右相似（2017年河南省中专学校报名）
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>同理，左右相似可得上下相似
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; border: 0px;>三、相似三角形常见解题技巧
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>1、三角形叉叉图（即三角形内部画一把叉）
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>此类题目常常考察求线段比例或者线段长度。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>图中四对线段比ae/ed、af/bf、cd/bd、ce/ef，知二求二。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>常用辅助线做法：过点作三角形边的平行线
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>遵循原则：所做辅助线不能破坏原有线段比例
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>2、三角形的可解性
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>在一个三角形中，必然存在三角、三边、三高、周长、面积这十一个量，若已知其中任意三个不全为角的条件，则可求出其他八个条件（简称portant; word-wrap: break-word !important; border: 0px;>知三求八）。
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>常见辅助线做法：作三角形边上的高
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>遵循原则：
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>①特殊角原则，即作高时常常把特殊角放在直角三角形中进行求解
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>②最长边原则，即作高时常常选择作最长边上的高，使得高在内部（2017年河南省中专学校报名）
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>③偶数边原则，即常常将偶数边作为直角三角形的斜边，方便计算
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>3、线段长度求法
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>①计算比：直接计算线段长度
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>做法：利用可解性直接求出所求比例线段的数值
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>②共线比：所求比例的两条线段在同一条直线上
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>做法：利用三角形叉叉图，构造平行线求解
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>③共三角形比：所求比例的两条线段在同一三角形中
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>做法：寻找或者构造与之相似且知内比的三角形进行求解
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>portant; word-wrap: break-word !important; border: 0px;>④相似比：所求比例的两条线段在两个相似三角形中（2017年河南省中专学校报名）
portant; word-wrap: break-word !important; font-family: 微软雅黑, 'microsoft yahei';>做法：找到两条线段所在的两个相似三角形，利用相似比求解
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