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 be said about sides SP and QR?

• A. Equal
• B. Parallel
• C. Both, equal and parallel
• D. Neither equal nor parallel

Answer 1

Answer: (A), (B)

The correct options are
A

Equal

B

Parallel

Join the diagonal BD 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

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

Thus, sides SP and QR are equal and parallel.