平面几何32讲

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。

周春荔，一直从事初等数学与数学教育、数学方法论与数学思想史、奥林匹克数学的综合研究与教学，有着丰富的竞赛选手及教练员培训的经验，主编或参编过许多适合中小学数学爱好者使用的教程、读本或资料，参加过多种竞赛的命题工作。北京数学奥林匹克学校的创始人之一，首任副校长，长期担任北京数学会普及工作委员会副主任，授课深入浅出，富有启发性，所写的数学普及读物和生动有趣的课堂教学很受青少年数学爱好者的欢迎。

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···············································&mi