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 (see Fig). Show that quadrilateral $BEFC$ is a parallelogram.

(N/A) To prove that $BEFC$ is a parallelogram.
Given that $BC = EF$ and $BC \parallel EF$.
$A$ quadrilateral is a parallelogram if one pair of opposite sides is equal and parallel.
Since $BEFC$ is a quadrilateral in which the pair of opposite sides $BC$ and $EF$ is equal and parallel,
Therefore,$BEFC$ is a parallelogram.