### Transformation of two squares in a square

We place the squares in agreement with the figure:

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

Transform polygon to square

It comes back to the Presentation