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

As we know the conditions of rhombus,

1. It should always be a parallelogram.

2. All the sides of the quadrilateral should be equal.

3. The diagonals are perpendicular to each other.

So here given only, “Diagonals of the quadrilateral are perpendicular to each other.”

Hence, we can’t say a given quadrilateral is always rhombus.

This is a quadrilateral with perpendicular diagonals which is not a rhombus.