Given: In quadrilateral ABCD, E, F, G and H are the mid-points of AB, BC, CD and DA respectively.
To Prove: EFGH is a parallelogram
Construction: Join AC
Proof: In ΔABC, E is the mid-point of AB and F is the mid-point of BC.
.
.. EF =
![](https://stream.philoid.co/assets/images/qa/user_files/63093/14902/images/Ex_files/10c2.gif)
AC and EF ïï AC...(i)
Similarly, HG =
![](https://stream.philoid.co/assets/images/qa/user_files/63093/14902/images/Ex_files/10c2.gif)
AC and HG ïï AC...(ii)
From eqns (i) and (ii), we get
HG ïï EF and HG = EF ...(iii)
.
.. EFGH is a parallelogram (One pair of opposite sides of a quadrilateral are equal and parallel.)