From the given figure, it is clear:

∠ABC = ∠FED (i)

Also,

∠BAC = ∠EFD (ii)

Therefore,

The two angles of ABC are equal to the two respective angles of FED

Also,

We know that:

Sum of interior angles of a triangle is equal to 180^o

Hence,

The third angle of both the triangles will also be equal

Thus,

∠BCA = ∠EDF (iii)

Therefore,

From (i), (ii) and (iii)

FED

By AAA congruence criterion