平行四边形的分类讨论问题时常出现在各地中考题中.在解答此类问题时,如果用纯几何的方法,则需要画图象,比较复杂,线条繁多,学生往往分类不完整,造成解答错误.笔者在教学中发现,在平面直角坐标系的条件下,可以用代数的方法来解答此类问题,这样分类清晰,不用画图形,学生容易掌握.一、预备知识如图1,在平面直角坐标系中,已知点A(a,b),B(c,d),C(c,d),D(m,n).如果四 Parallelogram classification discussion often appear in the test questions in various places in the solution of such problems, if the pure geometric method, you need to draw the image, more complicated, the line is numerous, the students are often classified as incomplete, resulting in the wrong answer. The author found in teaching, in the plane Cartesian coordinate system, you can use algebraic methods to answer such problems, so clear classification, do not draw graphics, students easy to master. First, the preparatory knowledge shown in Figure 1, Cartesian coordinates in the plane In the system, points A (a, b), B (c, d), C (c, d)