In $\Delta ABC$ and $\Delta DEF$,$AB = DE$,$AB \parallel DE$,$BC = EF$ and $BC \parallel EF$. Vertices $A, B$ and $C$ are joined to vertices $D, E$ and $F$ respectively. Show that quadrilateral $ABED$ is a parallelogram.

(N/A) To prove that $ABED$ is a parallelogram.
We know that a quadrilateral is a parallelogram if a pair of opposite sides is parallel and equal in length.
Given:
$AB = DE$
$AB \parallel DE$
In quadrilateral $ABED$,we have a pair of opposite sides ($AB$ and $DE$) which are both parallel and equal in length.
Therefore,$ABED$ is a parallelogram.