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近日翻阅一本初中几何教材，教材中把勾定理放在相似形中，用相似三角形证明勾定理，所派的辅助线是直角三角形斜边上的高线．怎样想到添这条辅助线的?编者没有写出，教参也没有说明，我觉得有点象“从帽子里跑出一支兔子”．为解决这个问题，我作了一些探索，结果是得到勾股定
Recently read a textbook for junior high school geometry. The teaching theorem put the theorem in a similar shape. The similarity triangle proves that the theorem. The auxiliary line is the high line on the hypotenuse of the right triangle. How do you think of adding this auxiliary line? The editor did not write it. The teaching reference did not say anything. I feel a bit like “Running a rabbit out of a hat.” In order to solve this problem, I made some explorations. The result is that