Challenge Level

Take any right-angled triangle with side lengths $a, b$ and $c$.

Make two enlargements of the triangle, by scale factors $a$ and $b$:

Rotate these triangles and fit them together to make a third triangle:

**Prove that the resulting triangle is an enlargement of the original triangle.**

What is the scale factor of enlargement of the resulting triangle?

Use what you have discovered about the side lengths of the resulting triangle to come up with a proof of Pythagoras' Theorem.