Pythagorean theorem proof (with leg rule)

In the applet below we have the right triangle ABC and we apply the leg rule: the steps show how to prove that the square on each leg is equivalent to the corresponding rectangle whose sides are the hypotenuse and the projection of the leg on it.

So if each square is equivalent to the corresponding rectangle ([math]AC^{^2}\doteq AH\cdot AB[/math] and [math]BC^2\doteq BH\cdot AB[/math])[br]the sum of the squares [math]\left(AC^2+BC^2\right)[/math] is equivalent to the sum of rectangles [math]\left(AH\cdot AB+BH\cdot AB\right)[/math][br][br]As you can see, the two rectangles together make the square on the hypotenuse [math]\left(AB^2\right)[/math].

Information: Pythagorean theorem proof (with leg rule)