“重建三角”正弦定理在全等三角形中的应用

The application of the sine theorem in “congruent triangles”

基于平面几何难学的现状,采用案例分析法探究“重建三角”实验方案中正弦定理在初中全等三角形中的两大应用:一是用正弦定理推导全等三角形的判定定理;二是应用正弦定理为部分特定的全等三角形题目提供简洁有利且无辅助线证明的方法。根据正弦定理在全等三角形中的应用,实现了几何“无辅”证明,将“无序”的问题变得程序化,这种程序化知识是以正弦定理为主线联结起来的,使得代数运算和几何演绎的思想一线串通。

Based on the current situation in which plane geometry is difficult to learn, this paper uses"case analysis method" to explore the two applications of sine theorem in "reconstruction triangle" experimental scheme in junior middle school. The first is to use the sine theorem to derive the judgment theorem of congruent triangle. The second is to use the sine theorem to provide a simple and advantageous method for proving some specific congruent triangles without auxiliary lines. According to the application of sinusoidal theorem in congruent triangles,"No auxiliary lines " proof of geometry is realized, and the "disorder" problem is programmed, which is connected by sinusoidal theorem and makes the idea of algebraic operation and geometric deduction concatenated.