Chapter 1.1, Problem 75AYU

Challenge Problem Geometry For any parallelogram prove that the sum of the squares of the lengths of the sides equals the sum of the squares of the lengths of the diagonals [Hints: Use $\left(0,0\right)$, $\left(a,0\right)$, $\left(a+b,c\right)$ and $\left(b,c\right)$ as the vertices of the parallelogram. Assume $a$, $b$ and $c$ are positive.]