为提高综合运用勾股定理及其逆定理解计算题和证明题的能力,现举数例说明如下:一、求长度例1 如图1,在△ABC中,AB=13,BD=5,AD=12,AC=15,求BC? 解:∵AD2+BD2=122+52=132=AB2,由勾股定理的逆定理知:∠ADB=90°,从而AD⊥BC,在Rt△ADC中,由勾股定理得:DC2=AC2-AD2=152-122=81,∴DC=9,从而BC= In order to improve the ability to comprehensively use the Pythagorean theorem and its inverse to understand calculations and proofs, several examples are given below. First, find the length Example 1 As in Figure 1, in △ABC, AB=13, BD=5, AD=12, AC=15, find BC? Solution: ∵AD2+BD2=122+52=132=AB2, know from inverse theorem of Pythagorean theorem: ∠ADB=90°, and thus AD⊥BC, in RtΔADC From the Pythagorean Theorem: DC2=AC2-AD2=152-122=81, ∴DC=9, and BC=