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Below is one of the many of Pythagoras Theorem proofs:

Let’s consider, for this demonstration,  two squares: one, ; the second  , smaller than  and inside the , as shown below.

The sides of the smaller square are making an angle, less than 90°, with the sides of the larger square.

The corners of the smaller square are on the sides of the larger square.

In between the two squares are four equal right triangles.

with b and c the right triangle’s legs and a its hypotenuse.

For proof of the above equality click here.

From above drawing it can be seen that:

But:

therefore, [1] becomes:

This means that:

(Pythagoras Theorem for the shown triangles)