Trapezoid law

A generalization of parallelogram law (we call it Trapezoid law), and a stronger result (diagonal formulas for expressing each diagonal of a trapezoid separately using its side lengths, we call it a Trapezoid theorem).

Theorem 1 

Trapezoid law (generalization of parallelogram’s law). We have $$a^ 2 + c^ 2 = e^ 2 + f ^2 − 2bd.$$Theorem 2

Trapezoid theorem (stronger result). We have 

$e^2 = bd + \dfrac{c ^2 b − a^ 2d}{b − d}$

$f^ 2 = bd + \dfrac{a ^2 b − c^ 2d}{b − d}$