Question

$\text{In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.}$

Answer 1

$\text{Given :}||\text{ABCD in which E and F are mid-points of AD and BC respectively.}\text{To Prove : BFDE is a}||gm.\text{Proof :}\because \text{E is mid-point of Ad. (Given)}\therefore DE=\frac{1}{2}AD\text{Also F is mid-point of BC}\left(Given\right)\therefore BF=\frac{1}{2}BCButAD=BC\text{(opp.~sides of}||gm)\therefore BF=DEAgainAD||Bc\Rightarrow DE||BFNowDE||BFandDE=BF\text{Hence BFDE is a}||gm.$