The pink triangle is a right triangle, because both yellow triangles are equilateral triangles (1,1,1) and (2,2,2), which constrains them to be equi-angular, too. The sum of all angles in a triangle is always 180, and an equilateral triangle has angles of (60,60,60). The straight line, ABC, displays an angle of 180 degrees. Thus, angle EBD is 60 degrees. Cos (EBD) = 0.5, but only if the pink triangle is a right triangle. As we can see, (BD)/(EB) = 0.5, so the Cos works and the pink triangle is, indeed, a right triangle.