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Question
In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.
Solution
Given: Parallelogram ABCD in which E and F are mid-points of AD and BC respectively.
To Prove: BFDE is a Parallelogram.
Proof: E is the mid-point of AD. (Given)
DE = `1/2`
Also, F is mid-point of BC (Given)
BF = `1/2`
But AD = BC (opp. sides of parallelogram)
BF = DE
Again AD || BC
⇒ DE || BF
Now DE || BF and DE = BF
Hence BFDE is a parallelogram.
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