初中教材人教版数学八年级下册第122页有这样一题:“四边形ABCD是正方形,点E是BC的中点,∠AEF=90°,EF交正方形外角平分线CF于F.求证:AE=EF.”(如图1)分析此题不难证明,只要取AB的中点G,连结EG,证明△AGE≌△ECF,问题即可得到解决.然而,当我们与学生一起对该题作进一步分析、发现、探究、联想、验证时,我们会从中体验到它的潜图1 There is a question like this: “The quadrilateral ABCD is a square, the point E is the midpoint of BC, ∠AEF = 90 °, and the square of the EF cross-square outer corner bisects CF in F. Evidence : AE = EF. ”(Figure 1) Analysis of the problem is not difficult to prove that as long as the midpoint of AB AB, EG, to prove △ AGE ≌ △ ECF, the problem can be solved. However, when we together with the students The topic for further analysis, discovery, exploration, association, verification, we will experience it from the latent image 1