Pythagoras Puzzler

Stage: 4 Challenge Level:

Take a square, and choose a point along one of the sides. Mark three more points, the same distance along each side, like this:

Now join from each point to the nearest corner on the opposite side of the square, like this:

It's possible to shade in a right-angled triangle:

Can you explain how I know the triangle has a $90^{\circ}$ angle?

Cut along the lines as shown below, and rearrange the pieces to make the L shape on the right.

Your L shape should look like a small square attached to a larger square. Can you describe the dimensions of the two squares in terms of the shaded right-angled triangle above?

Use these ideas to construct a proof of Pythagoras' Theorem. Are you convinced by your proof? Are others convinced by it? Send in your solution to see if it convinces the NRICH team!