Question

A quadrilateral ABCD is drawn in which the mid points of sides AB, BC, CD and AD are P, Q, R and S respectively.

If quadrilateral ABCD is a parallelogram, what can you say about quadrilateral PQRS ?

• A. Parallelogram
• B. Rhombus
• C. Rectangle
• D. Can’t say

Answer 1

The correct option is A

Parallelogram

SP = $\frac{1}{2}$BD ------------------ I

QR = $\frac{1}{2}$BD ------------------ II

PQ = $\frac{1}{2}$AC ------------------ III

RS = $\frac{1}{2}$AC ------------------ IV

Therefore, SP = QR (from I and II)

PQ = RS (from III and IV)

Therefore, opposite sides are equal and parallel. So, PQRS is a parallelogram.

We need to check whether opposite angles are of 90⁰ to determine if PQRS is a rectangle or a rhombus.

Since RS || AC and QR || BD, ∠AOB = ∠SRQ

We know that diagonals AC and BD bisect each other and do not intersect at right angles.

Therefore, PQRS is just a parallelogram.