Napoleon’s theorem states that if you erect equilateral triangles on the sides of an arbitrary triangle, the centers of those three equilateral triangles will form an equilateral triangle, too. In ...

A trapezoid has an area calculated by its height times one half the sum of its uneven sides. So the trapezoid has an area of ½ (a+b)(a +b). Since these areas are the same, this leads us to an ...