Proof of Pythagoras Theorem

The large squares above both have equal areas since both are of side

To produce the large square on the right arrange the red and blue triangles from the square above left around the outside as shown.

The area of the large square above left is given by

The area of the large square above right is given byor Equating these two gives

Expanding and simplifying givesand cancellingfrom both sides gives- this is Pythagoras theorem

Note thatare the sides of one of the red or blue right angled triangles, with being the longest side.