神奇的几何辅助线

章 几何证题知识概述 ······························································.1
1.1 命题的四种形式与充分必要条件 ············································.2
1.1.1 命题的四种形式 ························································.2
1.1.2 充分条件与必要条件 ···················································.4
1.2 分析数学题的思路 ·····························································.11
1.2.1 倒推分析思路 ··························································.11
1.2.2 分析综合思路 ··························································.13
1.2.3 反设分析思路 ··························································.15
1.3 几种数学解题探索方法 ·······················································.17
1.3.1 试验发现法 ·····························································.17
1.3.2 联想类比法 ·····························································.18
1.3.3 反例证伪法 ·····························································.19
1.3.4 数形结合的构造图形法 ···············································.19
第二章 神奇的几何辅助线 ·····························································.25
2.1 添加辅助线的目的 ·····························································.25
2.2 添加辅助线的原则 ·····························································.30
原则一 化繁为简 ·····························································.30
原则二 相对集中 ·····························································.31
原则三 作图构造 ·····························································.33
原则四 显现特殊性 ··························································.34
2.3 名题剖析智慧精华 ·····························································.35
2.4 图形变换与辅助线 ·····························································.38
2.4.1 应用平移变换添加辅助线 ············································.39
2.4.2 反射变换添加辅助线作法 ············································.50
2.4.3 通过旋转变换添加辅助线的作用 ···································.63
2.4.4 利用中心对称添加辅助线 ············································.73
2.4.5 利用相似变换添加辅助线 ············································.76
2.4.6 利用等积变换添加辅助线 ············································.78
2.4.7 构造圆进行添加辅助线 ···············································.80
2.4.8 利用复合变换添加辅助线 ············································.88
2.5 综合示范添加辅助线解题 ····················································.90
2.5.1 经典例题添加辅助线赏析 ············································.91
2.5.2 著名竞赛题添加辅助线选析 ·······································.109
2.5.3 一题多证添加辅助线例谈 ··········································.132
第三章 例说构造图形解题 ···························································.141
3.1 构造图形解几何题 ···························································.143
3.2 构造图形解三角题 ···························································.153
3.3 构造图形解代数题 ···························································.162