Parallelogram Law

Definition

$2(\Vert \mathbf{u}{\Vert }^2+\Vert \mathbf{v}{\Vert }^2)=\Vert \mathbf{u}+\mathbf{v}{\Vert }^2+\Vert \mathbf{u}-\mathbf{v}{\Vert }^2$ 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.