The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if

Options

A. PQRS is a rectangle
B. PQRS is parallelogram
C. diagonals of PQRS are perpendicular
D. diagonals of PQRS are equal

Answer

C

Explanation

Since, the quadrilateral ABCD formed by joining the mid-points of quadrilateral PQRS is a rectangle.
`therefore" "AC=BD" "["since, diagonals of a rectangular are equal"]`
`rArr" "PQ=QR`
Thus, quadrilateral PQRS is a rhombus.

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