本文用分析法确定线段内(外)分点的位置,给出平面几何中形如“a·b=c·d±e·f”型命题的一种证明方法,此法不但思路单纯、证法简便、易于掌握,而且突破了具有普遍意义的证明这种命题需要添置怎样的辅助线的难点.事实上,欲证线段a·b=c·d±e·f,若能在线段a(或b)上,确定一内外分点x_1、x_2,设分点到线段a(或b)的两个端点的距离分别为x、y,即令a=x±y,则欲证原命题只须证(x±y)·b=c·d±e·f,须证x·b±y·b=c·d±e·f,须证 In this paper, the position of the (outer) sub-point in the line segment is determined by analytical method, and a method for proving the proposition of the form “a·b=c·d±e·f” in plane geometry is given. This method is not only simple and The method is simple, easy to grasp, and breaks through the difficulty of demonstrating what kind of auxiliary line is necessary to prove that this proposition needs to be added. In fact, if you want to prove that the line segment a b = c d + e f, if line segment a ( Or b), determine an inner and outer points x_1, x_2, and set the distance between the two points of the points to the line segment a (or b) as x, y, that is, let a = x ± y, then the original propositions need to be proved. Certificate (x±y)·b=c·d±e·f, certificate x·b±y·b=c·d±e·f, certificate