The 120^{o} Rhombus (or Conjoined Twin Equilateral Triangles) Theorem

The 120^{o} Rhombus (or Conjoined Twin Equilateral Triangles) Theorem
Given a quadrilateral ABCD with three equilateral triangles ABE, BCF and CDG constructed on its sides, all inwardly or outwardly. If T_{1} and T_{3} are the respective centroids of ABE and CDG, and G_{2} is the centroid of EGF, then ∠T_{1}G_{2}T_{3} = 120°, and T_{1}G_{2} = G_{2}T_{3}. Further, if G_{4} is the centroid of EGH, then T_{1}G_{2}T_{3}G_{4} is a rhombus (consisting of two equilateral triangles T_{1}G_{2}G_{4} and T_{3}G_{2}G_{4} joined along mutual side G_{2}G_{4}).