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

Solution:

Given, the diagonals of a quadrilateral are perpendicular to each other.

We have to determine if the quadrilateral is a rhombus.

In a rhombus, opposite sides are parallel and the opposite angles are equal.

All the sides of a rhombus are equal in length.

The diagonals bisect each other at right angles.

If the diagonals are perpendicular to each other, then such a quadrilateral is not always a rhombus.

For a quadrilateral to be rhombus, the sides must be equal and the opposite angles must be equal.

Therefore, a quadrilateral is not always a rhombus if the diagonals are perpendicular to each other.

✦ Try This: The opposite angles of a parallelogram are (3x + 5)° and (61 - x)°. Find the value of all the four angles.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 173

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

Summary:

Diagonals of a quadrilateral are perpendicular to each other. Such a quadrilateral is not always a rhombus.

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