In ∆ABC, AD is median.

∴ BD = DC

We know that the line drawn through the midpoint of one side of a triangle and parallel to another side bisects the third side.

So, in ∆ABC, D is the mid point of BC and DE || BA.

Hence, DE bisects AC.

∴ AE = EC

This means that E is the midpoint of AC.

∴ BE is median of ∆ABC.