《几何辅助线》试读版.pdf

前言

我们知道，要想顺利解决几何问题，仅仅通过机械刷题是很难实现的，因为解决初中的

几何题要求学生必须有一定的解题经验积累、严谨的逻辑推理能力以及归纳总结能力。

大多数学生在面对几何题时，总会因它的图形变化多端而感到苦恼，难以下手。其实归

根到底还是因为不会作辅助线或辅助线作得不对。正确的辅助线可以将图形中分散的条件集

中，将隐藏的条件明朗化。因此，在解决几何题的过程中，所作辅助线的优劣在很大程度上

影响着解题速度和解题过程的难易程度。

学会添加辅助线是初中阶段很重要的一种解题方法，但辅助线的添加，不仅要求学生熟

练掌握各种图形的特征及性质，还要求学生有一定的思维创造性。本书聚焦初中数学几何辅

助线，以专题讲解为主，侧重方法和技巧的总结，旨在提高学生面对复杂几何问题时所具备

的几何推理能力，帮助学生快速找到问题的突破口，节省答题时间。

本书将初中阶段常考的几何问题涉及到的辅助线归纳为专题形式，每个专题辅助线归纳

全面清晰，包括分析已知条件（作辅助线的依据）、怎么作辅助线、得出结论和思路点拨，

教会学生掌握用辅助线方法解题，结合适当的练习达到熟练使用的程度。每个专题都配有典

型例题、针对训练和培优必练，题目类型全面多样，涵盖各种题型，由易到难分层训练，巩

固添加辅助线的技巧。

本书全国通用，题目精选全国各地近两年来七、八、九年级名校月考、期中考试和期末

考试、九年级的中考模拟考试、中考真题以及作者原创，好题绵延不断，方法简便，令人叹

为观止，适用于七、八、九年级的月考、期中考试、期末考试、九年级的中考模拟考试以及

中考复习。

宫尚宝

2023年8月20日

目录

第1章角平分线

1.1作垂线·············································································································1

1.2作平行线··········································································································3

1.3截取等线段·······································································································4

第2章中点

2.1构造中位线·······································································································9

2.2构造中线··········································································································11

第3章全等

3.1遇到中点倍长中线或作平行线···············································································18

3.2遇到平分线段作平行线························································································21

3.3构造共顶点旋转全等（手拉手）············································································23

3.4构造邻边相等对角互