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勾股定理神秘而美妙,它的证法多种多样,下面是教材中介绍的一种拼图证明勾股定理的方法.先做四个全等的直角三角形,设它们的两条直角边分别为a,b,斜边为c,然后按图1的方法将它们摆成正方形.

由图1可以得到(a+b)2=4×

1
2
ab+c2

整理,得a2+2ab+b2=2ab+c2

所以a2+b2=c2

如果把图1中的四个全等的直角三角形摆成图2所示的正方形,请你参照上述方法证明勾股定理.

上一题 下一题 0.0难度 选择题 更新时间:2017-04-14 04:36:39

答案(点此获取答案解析)

证明:∵S大正方形=c2,S大正方形=4S+S小正方形=4×
1
2
ab+(b﹣a)2
∴c2=4

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