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## 'Pythagoras Puzzler' printed from http://nrich.maths.org/

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!