Proof of Pythagoras’s theorem

Here we look at a proof using squares.

We want so show that h² = a² + b²

These two large outer squares are the same size. The areas are equal. There is an equal sign between the squares so show this. Both squares have sides of length a + b.

The square on the left is composed of the large blue square and four grey triangles.

The square on the right is composed of the yellow square and the red square and the same four grey triangles.

We can remove the four grey triangles from both large squares and the areas will still be equal.

This leaves us with the formula

h² = a² + b²