Question

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

Answer 1

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`