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'Matter of Scale' printed from http://nrich.maths.org/
Take any right-angled triangle with side lengths $a, b$ and
Make two enlargements of the triangle, by scale factors $a$
Rotate these triangles and fit them
together to make a third triangle:
You can use the interactivity below
to explore this problem. Choose a triangle, then click "New
Triangle" to make copies of your triangle, which can be enlarged
and rotated to fit together on the grey outline.
This text is usually replaced by the Flash movie.
Prove that the resulting triangle when the pieces are fitted
together is always 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'