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


Given:

The sides $AB$ and $CD$ of a parallelogram $ABCD$ are bisected at $E$ and $F$.

To do:

We have to prove that $EBFD$ is a parallelogram.

Solution:

Join $DE$, $BF$ and $EF$.


$ABCD$ is a parallelogram

This implies,

$AB = CD$

$AB \parallel CD$             (Opposite sides of a parallelogram are equal and parallel)

$EB \parallel DF$

$EB = DF$                 ($E$ and $F$ are mid points of $AB$ and $CD$)

Therefore,

$EBFD$ is a parallelogram.

Hence proved.

Tutorialspoint
Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

23 Views

Kickstart Your Career

Get certified by completing the course

Get Started
Advertisements