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.

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.

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