Question

Quadrilaterals formed by joining the mid- points of the sides of a quadrilateral PQRS taken in order, is a rectangle, if____.

• A. PQRS is a rectangle
• B. PQRS is a parallelogram
• C. Diagonal of PQRS are perpendicular
• D. Diagonals of PQRS are equal.

Answer 1

The correct option is C

Diagonal of PQRS are perpendicular

Since the quadrilateral, ABCD formed by joining the mid – points of quadrilaterals PQRS is a rectangle,

AC = BD [Diagonals of rectangle are equal]

PQ = QR

Thus, quadrilateral PQRS is a rhombus.

Hence, diagonal of PQRS i.e., PR and QS are perpendicular. [Since diagonals of rhombus are perpendicular to each other]