偶翻英文杂志“数学教师”(1961年12月),內中登載勾股定理的逆定理証法六种,頗有意思,茲介紹如下: 一、通常証法。 設在△ABC中,a~2+B~2=c~2。求証:∠C=90°。 証。作直角三角形A′B′C′使A′C′=b,B′C′=a,∠C′=90°,則 a~2+b~2=c′~2。根据已知条件a~2+b~2=c~2。∴c′=c~2因而c′=c。∴△ABC=△A′B′C′,因此 Even the English mathematics teacher “Mathematics teacher” (December 1961), published six kinds of inverse theorem of the Pythagorean theorem, which are quite interesting, are described as follows: First, usually the proof. Set in △ABC, a~2+B~2=c~2. Verification: ∠C=90°. certificate. As a right triangle A’B’C’, A’C’=b, B’C’=a, and ∠C’=90, a~2+b~2=c’~2. According to known conditions a~2+b~2=c~2. ∴c′=c~2 and c′=c. ∴ΔABC=ΔA′B′C′, so