True or false? Angle $B$in triangle A B C is obtuse. $D$ and $E$are the midpoints of sides AB and BC, respectively, and F is a point in side AC that is parallel to AB. BEFD is then a parallelogram.

 

Concept: Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Given: D is mid point of AB and  E is mid point of BC,F is any point on AC and  $EF\parallel AB$  Now, in  $∆ABC$, $E$

 is mid point of BC and  $EF\parallel AB$ By Mid point Theorem,  $F$ is mid point of AC

Also,  D is mid point of AB and  $F$ is mid point of AC

Hence, by mid point theorem,   $DF\parallel BE$ since,  $DF\parallel BE$ and  $EF\parallel AB OR BD$

Hence, BEFD is parallelogram.