In
mathematics, the simplest form of the
parallelogram law (also called the
parallelogram identity) belongs to elementary
geometry. It states that the sum of the squares of the lengths of the four sides of a
parallelogram equals the sum of the squares of the lengths of the two diagonals. Using the notation in the diagram on the right, the sides are (
AB), (
BC), (
CD), (
DA). But since in
Euclidean geometry a parallelogram necessarily has opposite sides equal, or (
AB) = (
CD) and (
BC) = (
DA), the law can be stated as,