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 

$e^2=bd+{\displaystyle \frac{c^{2}b-a^{2}d}{b-d}}$

$f^2=bd+{\displaystyle \frac{a^{2}b-c^{2}d}{b-d}}$