If in ∆ABC and ∆DEF, ABDE=BCFD, then ∆ABC ∼ ∆DEF when

Given: In $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}, \frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{FD}}$.

We know that if in two triangles, one pair of corresponding sides are proportional and the included angles are equal, then the two triangles are similar.

Then, $\angle \mathrm{B}=\angle \mathrm{D}$

Hence, $\triangle \mathrm{ABC}$ is similar to $\triangle \mathrm{DEF}$, we should have $\angle \mathrm{B}=\angle \mathrm{D}$.

Hence the correct answer is $(c)$.