论文部分内容阅读
定义有一角对应相等而另一角对应互补的两个三角形,称为等补三角形。 等补三角形广泛存在于下列几何图形中:(1)有内或外角平分线的任意三角形;(2)顶点与底边所在直线上任一点连线的等腰三角形;(3)有对角线的等腰梯形;(4)对角线平分一内角的圆内接四边形;(5)一组邻边相等的圆内接四边形。鉴于等补三角形的存在范围非常广泛,笔者研究了它的一些性质,本文介绍其中较为优美的几个,并例谈其在解题中的应用,供参考。 定理1 等补三角形中,相等角的对边与互补角的对边对应成比例。 证明如图1,等补△ABC和△A’B’C’中,
Define two triangles with one corner corresponding to the same and the other corner corresponding to each other. Equally filled triangles are widely present in the following geometries: (1) any triangle with bisectors of the inner or outer angles; (2) isosceles triangles connecting the vertices with any point on the straight line; and (3) with diagonal lines. Isosceles trapezoids; (4) Inscribed quadrilaterals in which the diagonal bisects an interior angle; (5) A set of adjacent quadrilaterals with equal sides. In view of the existence of a wide range of equal complement triangles, the author has studied some of its properties. This article describes some of the more elegant ones, and discusses their application in solving problems for reference. Theorem 1 In the complement triangle, the opposite sides of the equal angle are proportional to the opposite sides of the complementary angle. Prove that in Figure 1, etc. complement △ABC and △A’B’C’,