Having made this construction, we now transform the rectangle to the square. If the side of the rectangle is greater that the double of the side of the square, we cut the rectangle in congruent lesser rectangles successively and "we pile up" these, in order to form a new rectangle. This is done so that, later, the clippings will work well:
Having a rectangle with the longer side that is less than two times the side of the square of same area, the figure below indicates the cutting to be done:
The construction is the following one:
* we overlap the square to the rectangle and trace straight lines FC, ED and BG
* the colors in them indicate clippings from which we obtain the transformation.
As before, intuitively we can see that the parts cut in the rectangle fit perfectly in the square. Formally, we must show the congruences between the pairs of triangles GDJ and BHE, and DCH and JFE. To see the demonstration here click