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Why can the Pythagorean Theorem only be used with Right Triangles?

1 Answer

Apr 25, 2018

It's not really true. The Pythagorean Theorem (its converse, really) can be used on any triangle to tell us whether or not it is a right triangle.

Explanation:

For example, let's check the triangle with sides 2,3,4: #2^2+3^2=13 ne 4^2# so this isn't a right triangle.

But of course #3^2+4^2=5^2# so 3,4,5 is a right triangle.

The Pythagorean Theorem is a special case of the Law Of Cosines for #C=90^circ# (so #cos C= 0#).

# c^2 = a^2 + b^2 - 2 a b cos C #

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