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

No, if the diagonals of the quadrilateral are perpendicular to each other then such quadrilateral is not always a rhombus.

as you know conditions of rhombus

1. it should be parallelogram.

2. all sides should be equal.

3. diagonals are perpendicular to each other.

but here given only " diagonals of the quadrilateral are perpendicular to each other."

hence, we can't say given quadrilateral is always rhombus.