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.

Answer 1

heya mate nice question
here is your answer

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Answer 2

BFDE is a parallelogram.

Proved below.

Step-by-step explanation:

Given:

We have, ABCD as the given parallelogram. And  E is the mid-point of AD and F is the mid-point of BC.

Therefore in ∥gm ABCD,  

AD = BC  and AB = CD    [Opposite sides of ∥gm are equal]

Also AD∥BC and AB∥CD.

Now, AD = BC⇒$\frac{1}{2} AD = \frac{1}{2} BC$             [1]

Now, E is the mid point of AD and F is the mid point of BC.

So, AE = ED and BF = FC

Now, from (1), we have

AE = ED = BF = FC                                [2]  

In quadrilateral BFDE = DE    [Using (2)]

BF∥DE       [as, BC∥AD]

Therefore BFDE is a ∥gm. [In a quad, if a pair of opposite sides is equal and ∥, then it is a ∥gm]