【必考知识点】相似三角形

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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