|
|
|
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.
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.
Wikipedia: Thebault's theorem
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.
The webmaster and author of this Math Help site is Graeme McRae.