用三角形的面积公式S△A BC=12aha=21bhb=21chc,证明几何题,过程简捷,思路清晰,方法奇妙独特,对解决问题有事半功倍的效果。现略举几例供同学们参考。一、证线段相等例1已知梯形ABCD中,AB‖BC、M在CD上,且S△A B M=21S梯形A BCD,求证:M为CD的中点。分析:由图1,若过D、M分别作DE The area formula of the triangle SΔA BC=12aha=21bhb=21chc is used to prove the geometrical problem. The process is simple and clear, the idea is clear, the method is wonderful and unique, and it has a multiplier effect to solve the problem. Now give a few examples for the students. I. Equivalent to the line segment 1 In the known trapezoid ABCD, AB‖BC and M are on the CD, and SΔA B M=21S trapezoid A BCD. Prove that M is the midpoint of the CD. Analysis: From Figure 1, if over D, M, respectively, as DE