Question

Question 4
The quadrilateral 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) diagonals of PQRS are perpendicular
(D) diagonals of PQRS are equal

Answer 1

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

$\therefore$ AC = BD [since, diagonals of a rectangle are equal]

$\Rightarrow$ PQ = QR

Thus, quadrilateral PQRS is a rhombus.

Hence, diagonals of PQRS i.e., PR and QS are perpendiculars.

[since diagonals of rhombus are perpendicular to each other]