## Proof of Pythagoras Theorem

The above diagrams represent rearrangements of sets of shapes.

The blue triangles are all right angled, with the right angles at the corners of the yellow square, and congruent so all have the same area and the yellow squares are congruent so have the same area. We can find the area of the square on the left and equate it to the area of the rearrangement to the right.

The area of the large square on the left is

The area of the shape on the left is

Area of all the blue triangles together

Area of the yellow square

Area of the shape on the right is then

Equating the area of the shape on the left to the area of the shape on the right gives

This is exactly Pythagoras theorem. Note thatare the sides of a right angled blue triangle, with c the longest side opposite the right angle.