# Proving the converse of Pythagorus

• Sep 29th 2013, 05:55 PM
calculuskid1
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?

• Sep 29th 2013, 06:13 PM
chiro
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.
• Sep 29th 2013, 10:14 PM
ibdutt
Re: Proving the converse of Pythagorus
• Sep 30th 2013, 12:20 AM
Prove It
Re: Proving the converse of Pythagorus
Quote:

Originally Posted by calculuskid1
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...