We draw the segment BE and straight lines r and s perpendicular to the EB passing, respectively, through points E and B. Mark the point H where r intersects segment FG. We trace the perpendicular straight line to the EH passing through H and mark I the point of intersection of this straight line with s. Finally construct IJ perpendicular to the BG.

The colors in the figure indicate how to transform the given two squares , ABCD and ECGF, into the biggest square BEHI.
As before, intuitively we can see that the parts cut in the two lesser squares fit perfectly in the larger square.Formally we must prove the congruences between the pairs of triangles LAB and MJI, HGM and EDL, and FEH and JBC. To see the proof click here