Let the squares and share a common polygon
vertex.
The midpoints
and
of the segments and together with the centers of the original squares
and
then form another square . This theorem is a special case of the fundamental
theorem of directly similar figures (Detemple and Harold 1996).
Detemple, D. and Harold, S. "A Round-Up of Square Problems." Math. Mag.69, 15-27, 1996.Finsler, P. and Hadwiger, H.
"Einige Relationen im Dreieck." Comment. Helv.10, 316-326,
1937.Fisher, J. C.; Ruoff, D.; and Shileto, J. "Polygons and
Polynomials." In The
Geometric Vein: The Coxeter Festschrift. New York: Springer-Verlag, 321-333,
1981.
and 
share a common polygon
vertex 
.
The midpoints 
and 
of the segments 
and 
together with the centers of the original squares 
and 
then form another square 
. This theorem is a special case of the fundamental
theorem of directly similar figures (Detemple and Harold 1996).
