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【一轮复习】微专题:平面向量中的三角形“四心”问题

  • 2026-11-03 07:01:05
【一轮复习】微专题:平面向量中的三角形“四心”问题

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平面向量：三角形“四心”问题
27高考一轮复习

写在最前面——做可落地的课堂复盘。

从旧知巩固到新知过渡，从概念拆解到规律应用，我把每一堂课的思考与实践拆解存档，输出可复用、可落地的教学干货。

愿这些朴素的记录，能成为同行备课、教研的参考。

PART 01

板书设计

PART 02

课堂实录

一、引理—奔驰定理

GHMATHS

二、三角形“四心”

GHMATHS

PART 03

结论证明

一.三角形“四心”向量表达式证明过程

GHMATHS

二、奔驰定理的证明

GHMATHS

奔驰定理

由于其图形形状酷似奔驰车标，被戏称为奔驰定理。

奔驰定理： 已知  为  内任意一点，则有

证明

延长  交  于点 ，如上图。则有

则有，

即

PART 04

小试牛刀

●【AI赋能教学大赛】立体几何截面问题PPT分享
●【27高考·一轮复习】第27讲：解三角形
●【一轮复习】微专题：三次函数的性质及其应用
27高考·团子讲数学
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2026年《二年级上册数学期中复习七大专项合集》

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