Pythagorean Theorem and Areas of Squares

Drag the vertices of the triangle (A, B, abd C) and pay attention to the areas of the squares and the lengths of the sides of the triangle.

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After manipulating the vertices of the triangle...
1) What relationship exists among the areas of the squares?
2) Among the lengths of the sides of the triangle?
3) Can you formulalize your theory?

Michae Seiler, July 3, 2008, Created with GeoGebra