∵△ABC is an equilateral triangle, DE//AB, DF//AC,

∴∠ NDM = 60 (parallelogram diagonal is equal)

BD=FD (all three sides of an equilateral triangle are equal)

And △AFC are all equal to △CEB(SAS).

∴∠ACF =∠CFD =∠CBE (the corresponding angles of congruent triangles are equal, and the internal angles of two parallel lines are equal).

So △BDN is equal to △FDM(AAS).

△ DMN is an equilateral triangle.

If you think my answer is satisfactory, I hope to encourage me to adopt it! If you are not satisfied, you can continue to ask.