Question

The figure formed by joining the midpoints of the adjacent sides of a rhombus is a

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

Answer 1

The correct option is B Rectangle

In $△$ABC

$\Rightarrow$ PQ || AC

$\Rightarrow$ PQ = $\frac{1}{2}$AC . . . eq.1

In $△$ACD

$\Rightarrow$ SR || AC

$\Rightarrow$ SR = $\frac{1}{2}$AC . . . eq.2

From eq.1 and eq.2

$\Rightarrow$ PQ || SR & PQ = SR

Hence PQRS is parallelogram

Now, RS || AC & QR || BD.

Also AC $\perp$ BD

$\therefore$ RS $\perp$QR

Thus PQRS is a rectangle.