《平面幾何32講》是2023年電子工業出版社出版的圖書，作者是周春荔。
基本介紹
- 中文名：平面幾何32講
- 作者：周春荔
- 出版社：電子工業出版社
- 出版時間：2023年2月
- 頁數：368 頁
- 定價：96.80 元
- 開本：16 開
- ISBN：9787121449512
內容簡介,圖書目錄,
內容簡介
本書內容與國中、高中數學新編數學教材同步配套，把國中、高中數學中涉及到的全部平面幾何知識整合梳理到本書中，全書分為32講，每講都有基本知識講解，以及精選典型例題講解，作者為了能發散讀者數學思維，培養讀者平面幾何學習興趣，很多題目都進行了一題多解。本書是由作者多年給全國各地的學校做講座的內容改編而成的，內容經典、豐富、有趣，內容循序漸進，能滿足不同讀者的不同需求。想要梳理平面幾何知識的學生以及對平面幾何感興趣的讀者可閱讀此書。
圖書目錄
第 1 講 線段與角的推理計算························································.1
1.1 基礎知識······································································.1
1.2 典型例題精析································································.2
第 2 講 平行線與相交線推理························································.8
2.1 基礎知識······································································.8
2.2 典型例題精析································································.9
第 3 講 線段的性質····································································16
3.1 基礎知識······································································16
3.2 三角形不等式的簡單套用·················································17
3.3 簡單的不等式與極值·······················································20
第 4 講 三角形內角和問題···························································26
4.1 基本知識······································································26
4.2 三角形角的一些性質·······················································26
4.3 有關角的一些計算問題····················································28
4.4 綜合競賽題選析·····························································31
第 5 講 等積變形與面積計算························································37
第 6 講 三角形全等····································································48
6.1 三角形全等的基本例題····················································49
6.2 三角形全等的綜合例題····················································52
第 7 講 勾股定理及其套用···························································57
7.1 勾股定理及其逆定理·······················································57
7.2 勾股定理的各種套用·······················································59
第 8 講 三角形中位線定理套用·····················································67
8.1 基礎知識······································································67
8.2 基本例題······································································68
8.3 綜合例題······································································71
第 9 講 等腰三角形問題······························································76
9.1 基礎知識······································································76
9.2 基本證明練習題·····························································78
9.3 競賽題選講···································································82
第 10 講 正三角形綜合練習 ·························································86
第 11 講 平行四邊形的判定與性質 ················································97
第 12 講 梯形的判定與中位線定理 ·············································.108
第 13 講 正方形問題 ·······························································.118
第 14 講 四邊形中的趣味競賽題 ················································.128
第 15 講 平行截割定理 ····························································.140
第 16 講 相似三角形及其套用 ···················································.151
16.1 相似三角形的判定 ·····················································.151
16.2 相似三角形的性質 ·····················································.151
16.3 直角三角形的射影定理 ···············································.151
第 17 講 圓的基本問題 ····························································.166
17.1 圓的基本問題 ···························································.166
17.2 垂徑定理及其套用 ·····················································.168
17.3 和圓有關的角及其套用 ···············································.172
第 18 講 四點共圓及其套用 ······················································.181
18.1 四點共圓的基本競賽題 ···············································.181
18.2 四點共圓的綜合套用 ··················································.187
第 19 講 直線與圓 ··································································.194
第 20 講 圓冪定理 ··································································.203
第 21 講 正多邊形與圓 ····························································.210
第 22 講 幾何圖形不等式問題 ···················································.221
第 23 講 幾何極值問題 ····························································.238
第 24 講 等積變形與面積證題 ···················································.255
第 25 講 梅涅勞斯定理及其套用 ················································.273
第 26 講 塞瓦定理及其套用 ······················································.286
第 27 講 三角形的五心 ····························································.300
第 28 講 平移幫助你思考 ·························································.312
第 29 講 軸對稱給你智慧 ·························································.323
第 30 講 旋轉變換的藝術 ·························································.334
第 31 講 變換乘積與證題 ·························································.345
第 32 講 位似變換與證題 ·························································.354
