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 $ACFD$ is a parallelogram.

(N/A) Given: In $\Delta ABC$ and $\Delta DEF$,$AB = DE$,$AB \parallel DE$,$BC = EF$ and $BC \parallel EF$.
Step $1$: Consider quadrilateral $ABED$.
Since $AB = DE$ and $AB \parallel DE$,one pair of opposite sides is equal and parallel.
Therefore,$ABED$ is a parallelogram.
This implies $AD = BE$ and $AD \parallel BE$ (Opposite sides of a parallelogram are equal and parallel).
Step $2$: Consider quadrilateral $BCFE$.
Since $BC = EF$ and $BC \parallel EF$,one pair of opposite sides is equal and parallel.
Therefore,$BCFE$ is a parallelogram.
This implies $BE = CF$ and $BE \parallel CF$ (Opposite sides of a parallelogram are equal and parallel).
Step $3$: Consider quadrilateral $ACFD$.
From Step $1$,$AD \parallel BE$ and from Step $2$,$BE \parallel CF$. Thus,$AD \parallel CF$.
From Step $1$,$AD = BE$ and from Step $2$,$BE = CF$. Thus,$AD = CF$.
Since one pair of opposite sides ($AD$ and $CF$) is equal and parallel,quadrilateral $ACFD$ is a parallelogram.