The center overlap of two equilateral triangles is a symmetrical figure with the most symmetrical axis.

The triangle BCD and ABE are congruent, so AE=DC.

Triangle BMN is an equilateral triangle.

Proof: The main idea is to prove that MN is parallel to AB.

BM is the angular bisector, EM: MA = BE: BA (Angular bisector Theorem 2).

EN:NB = sinECD:sinBCD = SINCDB:sinBCD = BC:BD = BE:BA = EM:MA

So MN is parallel to AB.

BNM angle = 60

equilateral triangle