第一章 幾何證題知識(shí)概述 ······························································.1
1.1 命題的四種形式與充分必要條件 ············································.2
1.1.1 命題的四種形式 ························································.2
1.1.2 充分條件與必要條件 ···················································.4
1.2 分析數(shù)學(xué)題的思路 ·····························································.11
1.2.1 倒推分析思路 ··························································.11
1.2.2 分析綜合思路 ··························································.13
1.2.3 反設(shè)分析思路 ··························································.15
1.3 幾種數(shù)學(xué)解題探索方法 ·······················································.17
1.3.1 試驗(yàn)發(fā)現(xiàn)法 ·····························································.17
1.3.2 聯(lián)想類比法 ·····························································.18
1.3.3 反例證偽法 ·····························································.19
1.3.4 數(shù)形結(jié)合的構(gòu)造圖形法 ···············································.19
第二章 神奇的幾何輔助線 ·····························································.25
2.1 添加輔助線的目的 ·····························································.25
2.2 添加輔助線的原則 ·····························································.30
原則一 化繁為簡(jiǎn) ·····························································.30
原則二 相對(duì)集中 ·····························································.31
原則三 作圖構(gòu)造 ·····························································.33
原則四 顯現(xiàn)特殊性 ··························································.34
2.3 名題剖析智慧精華 ·····························································.35
2.4 圖形變換與輔助線 ·····························································.38
2.4.1 應(yīng)用平移變換添加輔助線 ············································.39
2.4.2 反射變換添加輔助線作法 ············································.50
2.4.3 通過旋轉(zhuǎn)變換添加輔助線的作用 ···································.63
2.4.4 利用中心對(duì)稱添加輔助線 ············································.73
2.4.5 利用相似變換添加輔助線 ············································.76
2.4.6 利用等積變換添加輔助線 ············································.78
2.4.7 構(gòu)造圓進(jìn)行添加輔助線 ···············································.80
2.4.8 利用復(fù)合變換添加輔助線 ············································.88
2.5 綜合示范添加輔助線解題 ····················································.90
2.5.1 經(jīng)典例題添加輔助線賞析 ············································.91
2.5.2 著名競(jìng)賽題添加輔助線選析 ·······································.109
2.5.3 一題多證添加輔助線例談 ··········································.132
第三章 例說構(gòu)造圖形解題 ···························································.141
3.1 構(gòu)造圖形解幾何題 ···························································.143
3.2 構(gòu)造圖形解三角題 ···························································.153
3.3 構(gòu)造圖形解代數(shù)題 ···························································.162