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 GRAPHICAL PROOF OF PYTHAGORAS THEOREM

This graphical 'proof' of the Pythagorean Theorem starts with the right triangle below, which has sides of length a, b and c. It demonstrates that a2 + b2 = c2, which is the Pythagorean Theorem.

1. Make 3 copies of the original triangle and arrange the four triangles in a square as shown. The outer square JKLM will remain fixed throughout the rest of the proof.
2. Each side of the empty square in the middle has a length of c, and so has an area of c2.
3. Re-arrange the triangles as shown so that the empty space is now divided into two smaller squares.
4. Notice that the top left empty square has each side equal to a, so its area is a2.
5. Notice also that the bottom right empty square has each side equal to b, so its area is b2.
6. Done. We have rearranged the triangles inside a constant-size square. The empty space we started with ( c2 ) must be equal to the sum of the two empty spaces at the end. Therefore a2+b2 = c2