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Math Help - Proving the converse of Pythagorus

  1. #1
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    Proving the converse of Pythagorus

    Prove that if a triangle has sides of lengths a, b and c, such that a2 + b2 = c2 then the triangleis right angled.
    The only thing i was thinking is cosing law. so
    a2 + b2-2abcos(x)= c2 and so -2abcos(x)=0 therefore x=90degrees



    Is there a more elegant way to prove this?



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  2. #2
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    Re: Proving the converse of Pythagorus

    Hey calculuskid1.

    You could prove it with inner products and norms but the way you have used is pretty good and a lot easier.
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    Re: Proving the converse of Pythagorus

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  4. #4
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    Re: Proving the converse of Pythagorus

    Quote Originally Posted by calculuskid1 View Post
    Prove that if a triangle has sides of lengths a, b and c, such that a2 + b2 = c2 then the triangleis right angled.
    The only thing i was thinking is cosing law. so
    a2 + b2-2abcos(x)= c2 and so -2abcos(x)=0 therefore x=90degrees



    Is there a more elegant way to prove this?



    I think that your way is very elegant. Of course, it would mean that you have to prove the Cosine Rule...
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