Varignon's Theorem, Proof Without Words

Let $BG=GD.$

The proof is by Alik Palatnik (Shaanan Academic Religious Teachers' College, Haifa, Israel), The College Mathematics Journal, Volume 48, Number 5, November 2017, p 354.

Alik Palatnik thanks an anonymous reviewer for pointing out that the proof of the perimeter result generalizes to arbitrary quadrilaterals, whereas the proof of the area result does not.

More on Varignon's parallelogram can be found on a separate page.