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在初中平面几何中,证明线段成比例的问题,是非常丰富多采的。证明中所采用的论据可以概括为两大类:其一,是利用相似三角形对应边成比例定理;其二,是利用平行线分线段成比例定理。对于具体问题,何时宜用第一类?何时宜用第二类?一般取决于成比例线段的端点位置的特征。本文介绍“三点定形法”揭示其中的一般规律性。
In the plane geometry of junior middle schools, the problem of proving the proportion of line segments is very rich. The arguments used in the proof can be summed up into two categories: the first is to use the proportional theorem of similar triangles; the second is to use the proportional theorem of parallel line breaks. When it comes to specific issues, when is it appropriate to use the first category and when it is appropriate to use the second category? Generally, it depends on the characteristics of the endpoint position of the proportional line segment. This article describes the “three-point setting method” to reveal the general regularity.