# Pythagorean Identity The Pythagorean Identity, also known as Pythagoras' Theorem, relates the lengths of the sides of a [[right-angled triangle]]. In a right-angled triangle with sides of length $a$, $b$, and $c$, with $c$ the [[hypotenuse]] then the following holds: $$ a^2 + b^2 = c^2 $$ This generalises to the [[cosine rule]] which holds for all triangles. [[!redirects Pythagoras Theorem]] [[!redirects Pythagoras theorem]] [[!redirects Pythagorean Identity]] [[!redirects Pythagorean identity]] [[!redirects Pythagoras' Theorem]] [[!redirects Pythagoras' theorem]] [[!redirects Pythagoras’ Theorem]] [[!redirects Pythagoras’ theorem]]