Question

In triangle ABC, D and E are mid-points of sides AB and BC respectively. Also, F is a point in side AC so that DF is parallel to BC. Prove that DBEF is a parallelogram.
Answer: DBEF is a parallelogram, If true then enter 1 else if False enter 0.

Answer 1

Given: D and E are mid points of AB and BC respectively. $DF\parallel BC$
Since, $DF\parallel BC$ D is mid point of AB.
By converse of mid point theorem, F is mid point of AC.
Now, E and F are mid points of BC and AC respectively.Thus, by mid point theorem,
$EF\parallel AB$ or $EF\parallel DB$
Since, opposite sides are parallel to each other. Hence, $DBEF$ is a parallelogram.