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由于直角三角形的三边满足平方关系,因此对于一些线段的平方关系的证明题,可设法寻找直角三角形,利用勾股定理进行证明.例1如图1,△ABC中∠BAC=90°,AB=AC,AD⊥BC于D.P是BC边上一点,PE⊥AB于E,PF⊥AC于E试说明:BE~2+CF~2=2DF~2.
Since the three sides of a right triangle satisfy the square relationship, we can try to find the right triangle by using the Pythagorean theorem to prove the squared relation of some lines. Example 1 As shown in Fig. 1, ABC = ∠ BAC = 90 °, AB = AC, AD ⊥ BC in the DP is a BC edge point, PE ⊥ AB in E, PF ⊥ AC in the E test shows: BE ~ 2 + CF ~ 2 = 2DF ~ 2.