不少几何题,虽然在给定的图形中没有明显的全等三角形,但我们可根据题目的特征巧妙地构造全等三角形,从而找到证题的思路. 一、平移法例1 已知△ABC中,AB=AC,E在AB上,F在AC的延长线上,且BE=CF,EF交BC于D,求证:DE=DF 分析:欲证DE=DF,图中无明显的全等三角形,这时可考虑去构造,过E作EG∥AF,交BC于G,只须证△DCF(?)△DGE即可. Many geometric questions, although there are no obvious congruent triangles in a given graph, but we can construct congruent triangles based on the characteristics of the topic, so as to find the train of thoughts. First, the translation method 1 is known in △ ABC , AB=AC, E is on AB, F is on AC’s extension line, and BE=CF, EF is transferred to BC on D. Proof: DE=DF Analysis: To prove that DE=DF, there is no obvious congruent triangle in the graph At this time, we can consider the structure, over E for EG ∥ AF, BC to G, only need to prove △ DCF (?) △ DGE.