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. Equal and parallel
• D. Neither equal nor parallel

Answer 1

The correct option is C

Equal and parallel

Join the diagonal BD of quadrilateral ABCD.

In ΔABD,
Since S is the mid-point of AD and P is the mid-point of AB, SP || BD and SP = $\frac{1}{2}$ BD (mid point theorem) --- (i)

In ΔBCD,
Since R is the mid-point of DC and Q is the mid-point of BC,
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.