Question

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 $BEFC$ is a parallelogram.

Answer 1

Data: In $\Delta ABC$ and $\Delta DEF$, $AB=DE,AB||DE,BC=EF$ and $BC||EF$.

Vertices $A,B$ and $C$ are joined to vertices $D.E$ and $F$ respectively.
Similarly, $BC=EF$ and $BC||EF$.
∴ $BE=CF$
$BE||CF$
∴ $BEFC$ is a parallelogram.