Prove that the quadrilateral formed by joining the midpoints of consecutive sides of rectangle is a rhombus and PLEASE PROVE THE VICE-VERSA ALSO.
To show that the quadrilateral formed by joining the mid point of the pair of adjacent sides of rectangle is a rhombus.
Here is the proof for the mentioned result:
Let ABCD is a rectangle such as AB = CD and BC = DA. P, Q, R and S are the mid points of the sides AB, BC, CD and DA respectively.
![](https://s3mn.mnimgs.com/img/shared/userimages/mn_images/image/Rh(1).png)
However, the diagonals of a rectangle are equal.
∴ AC = BD … (5)
By using equation (1), (2), (3), (4), and (5), we obtain
PQ = QR = SR = PS
Therefore, PQRS is a rhombus.