Question

In ${△}^{s}ABC$ and $DEF,AB\parallel DE;BC=EF$ and $BC\parallel EF$. Vertices, $A,B$ and $C$ are joined to vertices $D,E$ and $F$ respectively (see figure). Show that
quadrilateral $ABED$ is a parallelogram

Answer 1

Given : $\Delta ABC$ and $\Delta DEF,AB||DE;AB=DE;BC=EF;BC||EF$

To show : $ABED$ is a parallelogram

Proof :

Given that $AB=DE$ and $AB||DE$.

This implies one pair of opposite sides are equal and parallel to each other.

Therefore, $ABED$ is a parallelogram.