While I was having my breakfast I found this Geometry Proof on Instagram.
On two adjacent side of rectangle ABCD draw equilateral triangles CFD and BEC as shown. Prove the triangle AEF is equilateral.
Presh Talwalkar solved this by constructing some right-angled triangles and applying Pythagoras and algebra to show all three sides have equal length.
I approached the proof differently, without Pythagoras or any significant algebra. I'll put my solution in the Comment later on today.