Question

The diagonals of the quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Draw a rough figure to justify your answer.

Answer 1

Given : Diagonals are perpendicular.

If the diagonals are perpendicular then the quadrilateral need not necessarily be a rhombus.

Look at the figure, the diagonals are perpendicular to each other.

But all the sides are not equal.

PR ⊥ QS but PQ ≠ QR ≠ RS ≠ SP