三角形是最基本的几何图形之一,本文拟介绍三角形的一个性质,并运用类比推理的方法将该性质进一步推广到平面多边形和空间多边形.性质参见图1,图2,直线l分别交ΔABC三边所在直线AB,BC,CA于点A′,B′,C′,若AA′=a AB,BB′=b BC,CC′=c CA,则(1-a)(1-b)(1-c)=-abc.图1图2证明(1) The triangle is one of the most basic geometric figures. This article proposes to introduce a property of the triangle and use analogy inference to further extend this property to planar polygons and spatial polygons. See Figure 1 for the property, and Figure 2 shows the straight line l. The line AB, BC, CA is at the point A’, B’, C’, if AA’ = a AB, BB’ = b BC, CC’ = c CA, then (1-a) (1-b) ( 1-c)=-abc. Figure 1 Figure 2 Proof (1)