### 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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Graeme McRae.