Question

In triangle $ABC$, angle $B$ is obtuse. $D$ and $E$ are mid-points of sides $AB$ and $BC$ respectively and $F$ is a point on side $AC$ such that $EF$ is parallel to $AB$. Then, $BEFD$ is a parallelogram. State True or False.

• A. True
• B. False

Answer 1

The correct option is A True

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 $EF\parallel ABorBD$
Hence, BEFD is parallelogram.