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在给定的条件下,证明平面几何图形中的不等量关系,历来是初中学生的难点。证明几何不等式,一般是以几何中不等量的性质、公理、定理为基础,并借助于代数方法,三角方法、解析方法等,全面分析题设条件,灵活选取恰当方法,使问题获得解决。这里,通过若干例题和练习题,介绍平面几何里一些不等量关系的几种常见证明方法,供参考。一、基本证明方法证明两线段或两角的不等,基本的方法是使用一些有关的不等量公理和定理。
Given the conditions, it is always difficult for junior high school students to prove the unequal relations in plane geometry. The proof of geometric inequalities is generally based on the unequal properties of the geometry, axioms, theorems, and by means of algebraic methods, triangulation methods, analytical methods, etc., a comprehensive analysis of the title setting conditions, flexible selection of appropriate methods to solve the problem. Here, through a number of examples and exercises, introduce some common methods of proof for some unequal relations in plane geometry for reference. First, the basic proof method proves that the two lines or two angles are not equal. The basic method is to use some related unequal axioms and theorems.