Let the Squares and share a common 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).
See also Fundamental Theorem of Directly Similar Figures, Square
References
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.