本书内容与初中、高中数学新编数学教材同步配套，把初中、高中数学中涉及到的全部平面几何知识整合梳理到本书中，全书分为32讲，每讲都有基本知识讲解，以及精选典型例题讲解，作者为了能发散读者数学思维，培养读者平面几何学习兴趣，很多题目都进行了一题多解。本书是由作者多年给全国各地的学校做讲座的内容改编而成的，内容经典、丰富、有趣，内容循序渐进，能满足不同读者的不同需求。想要梳理平面几何知识的学生以及对平面几何感兴趣的读者可阅读此书。

第 1 讲 线段与角的推理计算························································.1 1.1 基础知识······································································.1 1.2 典型例题精析································································.2 第 2 讲 平行线与相交线推理························································.8 2.1 基础知识······································································.8 2.2 典型例题精析································································.9 第 3 讲 线段的性质····································································16 3.1 基础知识······································································16 3.2 三角形不等式的简单应用·················································17 3.3 简单的不等式与极值·······················································20 第 4 讲 三角形内角和问题···························································26 4.1 基本知识······································································26 4.2 三角形角的一些性质·······················································26 4.3 有关角的一些计算问题····················································28 4.4 综合竞赛题选析·····························································31 第 5 讲 等积变形与面积计算························································37 第 6 讲 三角形全等····································································48 6.1 三角形全等的基本例题····················································49 6.2 三角形全等的综合例题····················································52 第 7 讲 勾股定理及其应用···························································57 7.1 勾股定理及其逆定理·······················································57 7.2 勾股定理的各种应用·······················································59 第 8 讲 三角形中位线定理应用·····················································67 8.1 基础知识······································································67 8.2 基本例题······································································68 8.3 综合例题······································································71 第 9 讲 等腰三角形问题······························································76 9.1 基础知识······································································76 9.2 基本证明练习题·····························································78 9.3 竞赛题选讲···································································82 第 10 讲 正三角形综合练习 ·························································86 第 11 讲 平行四边形的判定与性质 ················································97 第 12 讲 梯形的判定与中位线定理 ·············································.108 第 13 讲 正方形问题 ·······························································.118 第 14 讲 四边形中的趣味竞赛题 ················································.128 第 15 讲 平行截割定理 ····························································.140 第 16 讲 相似三角形及其应用 ···················································.151 16.1 相似三角形的判定 ·····················································.151 16.2 相似三角形的性质 ·····················································.151 16.3 直角三角形的射影定理 ···············································.151 第 17 讲 圆的基本问题 ····························································.166 17.1 圆的基本问题 ···························································.166 17.2 垂径定理及其应用 ·····················································.168 17.3 和圆有关的角及其应用 ···············································.172 第 18 讲 四点共圆及其应用 ······················································.181 18.1 四点共圆的基本竞赛题 ···············································.181 18.2 四点共圆的综合应用 ··················································.187 第 19 讲 直线与圆 ··································································.194 第 20 讲 圆幂定理 ··································································.203 第 21 讲 正多边形与圆 ····························································.210 第 22 讲 几何图形不等式问题 ···················································.221 第 23 讲 几何极值问题 ····························································.238 第 24 讲 等积变形与面积证题 ···················································.255 第 25 讲 梅涅劳斯定理及其应用 ················································.273 第 26 讲 塞瓦定理及其应用 ······························