A quick proof, by construction, of the first part of this result goes as follows: consider a rotation of π/3 radians about the point C that maps point A to point B, and M to M . Clearly, △MCM ′ is equilateral and MM ′ = MC. Since MA = M B, we conclude that △MBM ′ has sides equal to MA,MB, and MC (see Figure 1; all marked angles are equal to π/3 radians). The theorem is not classical in that not...