论文部分内容阅读
辅助线是建立在已知和未知之间的一座桥梁,是开启学生创造性思维的一把钥匙. 在已掌握的知识基础上,适当地添置辅助线可构成使用某个公理或定理的条件,或激活思维增加解题可能性,打开解题的突破口.下面针对一道竞赛题的多种添线及证明方法加以说明. 题目:如图1,已知△ABC中,AB=AC,BE⊥BC,CF⊥BC,过点A的直线分别与BE、CF交于点E、F. 求证:AE=AF.分析:注意到待证的两条线段在同一直
Auxiliary line is a bridge established between known and unknown. It is a key to open the students’ creative thinking. Based on the acquired knowledge, the appropriate addition of auxiliary lines can form the conditions for using a certain axiom or theorem, or Activate the thinking to increase the probability of problem solving and open up the breakthrough point for problem solving. Below is a description of multiple lines and proof methods for a competition problem. Title: As shown in Figure 1, known as △ABC, AB=AC, BE⊥BC, CF ⊥ BC, the straight line crossing point A and BE and CF are intersected at points E and F. Proof: AE=AF. Analysis: Note that the two line segments to be proved are in the same line.