北师大版教材八年级下册《平行四边形》中有这样一个命题判断:“一组对边相等,一组对角相等的四边形是平行四边形”.大家知道,这是一个假命题,但如何构造反例图形却是一道难题!教学中有不少教师给学生介绍了下面的构图方法:如图1,作一个等腰△ABC,在底边BC上取一点D(不能是中点,你知道为什么吗?),连结AD,作AD的垂直平分线l,以l为对称轴 Beijing Normal University version of the eighth grade textbook “Parallelogram” in the judgment of such a proposition: “A group of equal sides, a group of diagonally equal quadrilateral is a parallelogram.” We all know, this is a fake proposition, However, how to construct counterexamples is a difficult problem! Many teachers in teaching teach students the following composition methods: As shown in Figure 1, make an isosceles ABC, take a point D on the bottom edge BC (can not be the midpoint, Do you know why?), Link AD, AD vertical bisector l, with l as the axis of symmetry