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© Copyright 2003, Jim Loy
Here is a proof of the Pythagorean Theorem, using dissection. Move the two red dots to change the shape of the right triangle at the bottom. The green and yellow triangles are exact copies of this right triangle. If the legs of this triangle are a and b, then you should see that the area of the figure above left (two squares, stuck together) is a^2+b^2 (where a^2 means a squared). And with the hypotenuse being c, then the square above right has an area of c^2. But the top left figure has been dissected to form the top right figure, and so they have the same area: a^2+b^2 = c^2.
The above Java interactive demonstration was created with Cinderella (a geometry program).
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