Diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Give a figure to justify your answer.

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Solution

False, it is not necessary that a quadrilateral having perpendicular diagonals is a rhombus.
e.g. Consider a trapezium ABCD in which $A B ∥ C D$ .

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Similar questions

The quadrilateral formed by joining the midpoints of the sides of a quadrilateral ABCD, taken in order, is a rhombus, if

(a) ABCD is a parallelogram

(b) ABCD is a rhombus

(d) diagonals of ABCD are perpendicular to each other

Is quadrilateral ABCD a rhombus?

I. Quadrilateral ABCD is a ||gm.

II. Diagonals AC and BD are perpendicular to each other.

The correct answer is: (a)/(b)/(c)/(d).

In the figure below, the diagonals of the quadrilateral ABCD are perpendicular to each other.

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