please solve question number 2 and show full process

Dear student,

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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