论文部分内容阅读
有关比例线段的证明,主要分布在初中几何第四章相似形及第五章圆内。按其线段所在的位置可分两大类型:一是所要证明的线段不在一直线上;二是所要证明的线段在一直线上。证明这类问题的主要依据是:比例的性质,平行截割比例线段定理,相似三角形的性质,三角形内(外)角平分线的性质,以及直角三角形中的比例线段定理,圆幂定理等。本文想就这类问题的证明思路作一简单探讨。一、所要证的成比例的线段不在一直线上这类问题的解题思路首先是考虑所要证
The proof of the proportional line segment is mainly distributed in the similar shape of the fourth chapter of the junior middle school geometry and the fifth chapter circle. According to the position of the line segment, it can be divided into two types: one is that the line segment to be proved is not in a straight line; and the other is that the line segment to be proved is in a straight line. The main basis for the proof of this kind of problem is: the nature of proportions, the line segment theorem of parallel cutting ratios, the nature of similar triangles, the nature of bisect (external) angle bisectors in triangles, and the propositional line theorem and the circle power theorem in right triangles. This article wants to make a simple discussion on the proof of this type of problem. First, the questionable line of thought for which the proportioned line segment to be proved is not on the line is to first consider the required proof.