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

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 degrees about its center

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

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

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 degrees about its center - a PWW

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
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