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(一) 初中几何课本第二册“相似形”这一章的第四节写的是“三角形一边的平行线的判定”、它是在证明了“平行于三角形一边的直线截其他两边所得的对应线段成比例”这一命题的逆命题:“如果一条直线截三角形的两边,其中一边上截得的一条线段和这边与另一边上截得的一条对应线段和另一边成比例那么这条直线平行于第三边”。由于原命题的结论(比例线段)不只一种,从而其逆命题的条件(比例线段)也不只一种,即除上述一种形式外,还有如下形式。如图(1)在△ABC中。若AD/DB=AE/EC,则DE//BC由上述定理,根据比例性质易证后一种形式的逆命题为真。就得到了推论:若一条直线截三角形的两边所得的对应线段成比例那么这条直线平行于三角形的第三边。
(a) In the fourth section of the “similar form” in the second volume of the textbook of junior high school geometry, “the judgment of the parallel line on one side of the triangle” is written, which proves that “the line parallel to one side of the triangle cuts the other two sides. The inverse proposition of the proposition that the corresponding line segment is proportional: “If a line cuts two sides of a triangle, where one line segment on one side is proportional to a corresponding line segment and the other side on the other side then this is The straight line is parallel to the third side.” Since the conclusion of the original proposition (proportional line segment) is not only one, the condition of the inverse proposition (proportional line segment) is also not only one, that is, in addition to the above-mentioned one form, there are the following forms. Figure (1) is in △ABC. If AD/DB=AE/EC, then DE//BC is true by the above theorem, according to the proportional nature of the converse of the latter form. It is inferred that if the corresponding line segments obtained from the two sides of a straight truncated triangle are proportional then this line is parallel to the third side of the triangle.