Question

The sides AB and CD of a parallelogram ABCD are bisected at E and F .prove that EBFD is a parallelogram

Answer 1

hope it helps you ...this the answer...naming varies...

Answer 2

EBFD is a parallelogram.    

Proved below.

Step-by-step explanation:

Given:

Here we are given that  the sides AB and CD of a parallelogram ABCD are bisected at E and F.

Now as shown in the figure given below,

AB || DC and AB = DC   [ opposite sides of a parallelogram ]

There fore EB || DF and $EB =\frac{1}{2} AB$    [ E is the mid point of AB ]

Also,

$DF = \frac{1}{2} DC = \frac{1}{2} AB$   [F is mid point of DC and DC = AB]

Therefore EB || DF and EB = DF

EBFD is a parallelogram.   [One pair of opposite sides is parallel and equal]

Hence proved.