D and E are the mid-points of the sides AB and AC,

(c) in $\triangle A D E$ and $\triangle C F E$, suppose $D E=E F$

Now.      $A E=C E$    [since, $E$ is the mid-point of $A C$ ]

Suppose $D E=E F$

and $\quad \angle A E D=\angle F E C \quad$ [vertically opposite angles]

$\begin{array}{lll}\therefore & \Delta A D E \cong \triangle C F E & \text { [by SAS congruence rule] }\end{array}$

$\begin{array}{lll}\therefore & A D=C F & \text { [by CPCT rule] }\end{array}$

and     $\angle A D E=\angle C F E$    [by CPCT]

Hence, $A D \| C F$   [since, alternate interior angles are equal]

Therefore, we need an additional information which is $D E=E F$