Show that the quadrilateral, formed by joining the mid-points of the sides of a square, is also a square.

Explanation

Given: In a square ABCD, P, Q, R and S are the mid-points of AB, BC, CD and DA, respectively.

To Prove: PQRS is a square.

Construction : Join AC and BD

Proof : ABCD is a square

AB = BC = CD = AD

Also, P, Q,R and S are the mid-points of AB, BC, CD and DA, respectively.

In `triangleADC`, `SR|\|AC`

`SR=1/2AC`(By mid-point theorem)

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