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在平面几何证题中,除少数题外,多数题都必须引辅助线,使已知“条件”和“求证”发生联系,在条件与结论间架起一座桥梁,得到新的图形和新的关系,便于应用定理进行证明。本文就三角形内常用辅助线的一些规律,谈一点自己的体会。一、三角形角平分线问题:(1)常用“角平分线上的点到角的两边距离相等”的定理,作一边上某特殊点对于角平分线的对称点。(2)作外接圆,造成等弧、等弦、弦心距相等的条件。
In plane geometry test questions, with the exception of a few questions, most questions must lead to auxiliary lines, so that the known “conditions” and “proofs” are related, and a bridge is built between conditions and conclusions to obtain new figures and new relationships. To facilitate the application of theorem to prove. This article discusses some of the rules of commonly used auxiliary lines in triangles and discusses their own experiences. 1. Triangular angle bisector problem: (1) Theorem commonly used for “equal distances from point to angle on the angle bisector” is used as a symmetry point for a particular point on the side of the bisector. (2) As a circumcircle, conditions such as equal arc, equal string, and string center distance are created.