In ∆ABC and∆DEF, if ∠A -∠D, ∠B = ∠E and AB = EF, then are the two triangles congruent? If yes, by which congruency criterion?

No, criterion of congruence of triangles ( AAS, ASA, RHS ) is not applicable on ∆ABC and ∆DEF.

Hence, ∆ABC and ∆DEF are not congruent.