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等积式证明是初中平面几何常见题型之一,由于这类题型灵活,形式多样,有些还有一定的难度,因此,对开发学生智力,培养学生分析、解决问题、逻辑推理能力都将起到积极的作用,本文试图通过对一些题目的证明介绍等积式证明的几种常用方法。一利用相似三角形 [例1] 已知Rt△ABC,∠C=90°,AC>BC,o是BA的中点,FO⊥AB交AC于E,交BC的延长线于F,求证:OC~2=EO·FO。
The proof of isomorphism is one of the common problems in the plane geometry of junior high school. Because of the flexibility and diversity of these types of questions, there are certain difficulties. Therefore, the ability to develop students’ intelligence, develop student analysis, solve problems, and logically reason Playing an active role, this article attempts to introduce several common methods for the proof of isomorphism through the proof of some topics. A similar use of triangles [Example 1] known Rt △ ABC, ∠C = 90 °, AC> BC, o is the midpoint of BA, FO ⊥ AB cross AC in E, the extension of the line BC in F, verification: OC ~2=EO·FO.