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. Solve the following questions.

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

• A. Rectangle
• B. Square
• C. Rhombus
• D. Parallelogram

Answer 1

The correct option is D

Parallelogram

Join the diagonals BD and AC of quadrilateral ABCD.

In ΔABD , SP || BD and SP = $\frac{1}{2}$ BD (mid point theorem) ------- I

In ΔBCD , QR || BD and QR = $\frac{1}{2}$BD (mid point theorem) ------- II

In ΔACD , RS || AC and RS = $\frac{1}{2}$ AC (mid point theorem) -------- III

In ΔABC , PQ || AC and PQ = $\frac{1}{2}$ AC (mid point theorem) ---------IV

From I and II , SP || QR and SP = QR ---------------------------------------- V

From III and IV , RS || PQ and RS = PQ ---------------------------------------- VI

From V and VI , PQRS is a parallelogram since opposite sides are equal and parallel.