Question

The figure obtained by joining the mid- points of the sides of a rhombus, taken in order is .

• A. a square
• B. a trapezium
• C. a rhombus
• D. a parallelogram

Answer 1

The correct option is D a parallelogram

Let ABCD be a rhombus and P, Q, R and S be the mid-points of sides AB, BC, CD and DA respectively.

By mid point theorem,
As, SP$\parallel$ BD and SP $=\frac{1}{2}$ BD
and, RQ$\parallel$ BD and RQ $=\frac{1}{2}$ BD
$⟹$ Opposite sides are equal and parallel.
So, PQRS is a prallelogram.