How do squares of the sides of a triangle, any triangle, relate?
The general rule that relates the sides of a triangle is called the law of cosines. It regards the following situation, where you know an angle of the triangle and want to relate the side lengths:
It is stated as follows: $$C^2=A^2+B^2-2AB\cos(\alpha).$$ Note that this has a very similar form to the Pythagorean theorem - just with an extra adjustment for the angle $\alpha$. In particular, if $\alpha$ is a right angle, this last term is zero, so it reduces to the Pythagorean theorem. The equation also tells us that when $\alpha$ is obtuse, the opposite is longer than it would be in a right triangle and when $\alpha$ is acute, the opposite side is shorter.