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

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 $\cos C = 0$).

${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$