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Thebault's Problem 1

Line segments connecting centers of squares on sequential sides of a parallelogram form a square.  This is a special case of van Aubel's Theorem.

Thebault's Problem 2

The vertices of equilateral triangles constructed on the outside (or inside) of two consecutive sides of a square, together with the "untouched" vertex of the square form an equilateral triangle.

Internet references

Wikipedia: Thebault's theorem 

Related pages in this website:

Summary of geometrical theorems

Van Aubel's Theorem: Line segments connecting centers of squares on opposite sides of a quadrilateral are perpendicular and equal in length.  (See also van Aubel's second theorem.)

Napoleon's Theorem: if equilateral triangles are constructed on the sides of any triangle (all outward or all inward), the centers of those equilateral triangles themselves form an equilateral triangle.


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