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在平面几何中,求证线段之间的等量关系的问题,主要有如下两类:第一类,如求证线段相等,求证线段之间的倍分关系,求证比例线段(或等积线段),求证线段的复比(即几个比的乘积)相等,所有这些,都可以归结为求证线段的比或复比等于1的问题;第二类,如求证线段之间的和差关系,求证线段的积(或比)之间的和差关系,所有这些,都可以归结为求证线段的比或复比的代数和等于1的问题。
In plane geometry, the problem of equivalence between line segments is mainly classified into the following two categories: The first category, such as the verification of line segments equal to the line-doubling relationship between line segments, to verify proportional line segments (or congruent line segments), The complex ratio of the verification line segment (that is, the product of several ratios) is equal, all of which can be attributed to the problem that the ratio or complex ratio of the verification line segment is equal to 1; the second category, such as the relationship between the line and the difference of the verification line segment, the verification line segment. The relationship between the product (or ratio) and the difference between them, all of which can be attributed to the problem of verifying the linear or complex ratio of the algebraic sum equal to one.