Because point f is the midpoint of the CD.

So CF=FD

Because AB=AE, ∠ABC=∠AED, BC=ED, CF=FD.

Therefore, triangle ABC and triangle AED are congruent (SAS)

So AC=AD, angle BAC= angle EAD.

Because f is the midpoint of the side CD of the isosceles triangle ACD

An isosceles triangle with three lines in one

So angle CAF= angle DAF

Angle BAF= angle EAF

That is, AF bisection ∠BAE