Geometry Problem 1369: Equilic Quadrilateral, Congruence, Midpoint,
60-120 Degrees Rhombus or Polyiamond

In the figure below ABCD is an
equilic quadrilateral.
Prove that the midpoints E, G, F, and H of the
diagonals and the sides BC and AD always determine a 60-120
degrees rhombus or polyiamond (diamond).