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证明比例线段是平面几何问题常见的类型,其题断一般为a:b=c:d,ab=cd及b~2=ac。后两类一般可转化为第一类来分析。通过有关比例线段问题的分析、证明,可使学生把全等形、相似形、圆等知识有机地结合、融会贯通,有利于培养学生综合运用知识及方法的良好习惯,提高分析问题的逻辑思维能力。因此证明比例线段既是初中几何的重点又是难点,本文通过举例就证明思路作点探讨。
It is proved that the proportional line segment is a common type of plane geometry problem, and its abbreviation is generally a:b=c:d, ab=cd and b~2=ac. The latter two categories can generally be converted into the first category for analysis. By analyzing and proving the problem of the proportional line segment, students can integrate and integrate the knowledge of isomorphism, similarity, and round, which will help students develop good habits of comprehensive use of knowledge and methods, and improve their logical thinking ability. . Therefore, it is proved that the proportional line segment is both the focus and the difficulty of the junior middle school geometry.