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 $ACFD$ is a parallelogram.

Answer 1

In a quadrilateral $ACFD,$
$AD=CF$
$AD||CF$ (proved)
$\therefore AC=DF$
$AC||DF$
$\therefore ACFD$ is a parallelogram.