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勾股定理是几何学中一个很重要的定理,它的应用非常广泛,初学勾股定理时,难免会出现这样或那样的错误,我们一定要认真剖析致误原因,做到防微杜渐,常见的错误类型如下：1前提不清,错误入侵。例1已知△ABC各边长均为整数,且AC=4,BC=3,AB是最长边,则AB的长为( )。A．5 B．6 C．7 D．5或6错解：由勾股定理,得AB= (AC~2+BC~2)~(1/2)=(4~2+3~2)~(1/2)=5．故选A．
The Pythagorean theorem is a very important theorem in geometry. Its application is very extensive. When learning the Pythagorean Theorem, it is inevitable that this or that error will occur. We must carefully analyze the cause of the error, so as to prevent it from becoming a common mistake. The types are as follows: 1 The premise is unclear and the error is invaded. In Example 1, it is known that the length of each side of △ABC is an integer, and AC=4, BC=3, and AB is the longest side. Then, the length of AB is (). A. 5 B. 6 C. 7 D. 5 or 6 misunderstanding: From the Pythagorean theorem, AB=(AC~2+BC~2)~(1/2)=(4~2+3~2)~(1/2)=5. So choose A.