# In the Spirit of Thébault I

Dr. Ray Viglione from Kean University and his undergraduate student Purna Patel found a variation of Victor Thébault's first problem that dealt with the configuration of squares built on the sides of a parallelogram.

Given a parallelogram, the centers of the squares drawn on both sides of both diagonals form a parallelogram congruent to the original and rotated $90^{\circ}$ about its center

The applet below serves to illustrate the problem and its solution:

22 January 2015, Created with GeoGebra

As a backup for the GeoGebra applet, below is a plain diagram for a solution without words.

### References

1. Purna Patel, Raymond Viglione, Proof Without Words: A Variation on Thébault's First Problem, The College Mathematics Journal, Vol. 44, No. 2 (March 2013), p. 135

### Thébault's Problems

• Thébault's Problem I
• Thébault's Problem II
• Thébault's Problem III
• Y. Sawayama's Lemma
• Jack D'Aurizio Proof of Sawayama's Lemma
• Y. Sawayama's Theorem
• Thébault's Problem III, Proof (J.-L. Ayme)
• Circles Tangent to Circumcircle
• Thébault's Problem IV
• A Property of Right Trapezoids
• A Lemma on the Road to Sawayama
• Excircles Variant of Thébault's Problem III
• In the Spirit of Thebault I
• Dao's Variant of Thebault's First Problem