This beautiful proof of the ancient theorem of Pythagoras is attributed to Leonardo de Vinci. There should be no need for words of explanation, but I have added them all the same.
This proof of the irrationality of root 2 uses geometry to gain the contradiction.
Friendly triangles – good visual method for memorising trig ratios of 30, 45 and 60 degree angles. Known for thousands of years as per the Babylonian tablet