Euclid's Proof of the Pythagorean Theorem
Euclid's Proof of the Pythagorean Theorem
The top two sliders choose lengths of the legs of the right triangle.
The third slider converts the squares on the legs of the right triangle into parallelograms with equal area and vertical sides. The top of each square slides along a line parallel to the leg of the triangle that forms its base until the adjacent sides are vertical.
The fourth slider slides the parallelograms down so that they become rectangles occupying the square on the hypotenuse. The parallelograms, in addition to being equal in area to the squares on the legs, have areas equal to these two rectangles that together can form the square on the hypotenuse.