不论是华东师大版还是北师大版初中数学课本,在学习了三角形全等和命题证明之后,会有一些证明题作为经典题目出现,而且问题不断变化、提升,对学生能力的考查也不断提高。例如下面这道证明题,已经发生了三次变化。题目1:如图1,已知四边形ABCD中,∠1=∠2,∠3=∠4,AD+BC=AB,求证:AD∥BC.题目2:如图1,已知四边形ABCD中,∠1=∠2,∠3=∠4,(1)如果AD+BC=AB,求证: Whether it is the East China Normal University version or the junior high school math textbooks, after learning the triangle congruent and proof of proposition, there will be some proof questions as classic topics appear, but the problem is constantly changing, upgrading, examining the ability of students also continue improve. For example, the following proof shows that three changes have taken place. Problem 1: As shown in Fig. 1, it is known that the quadrilateral ABCD, ∠1 = ∠2, ∠3 = ∠4, AD + BC = AB, ∠1 = ∠2, ∠3 = ∠4, (1) If AD + BC = AB, verify: