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# Diagonals of a rhombus are equal and perpendicular to each other. Is this statement true? Give reason for your answer

**Solution:**

Consider a rectangle ABCD

In a rectangle we know that

AB = CD and AD = BC

Here

AC² = AD² + CD²

If AD = BC

AC² = BC² + CD²

AC² = BD²

Taking square root on both sides

AC = BD

The diagonals AC and BD are equal to each other but we cannot consider it to be perpendicular

Therefore, the statement is false.

**✦ Try This: **MNOP is a parallelogram. If its diagonals are equal, then find the value of ∠MNO.

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.2 Sample Problem 2**

## Diagonals of a rhombus are equal and perpendicular to each other. Is this statement true? Give reason for your answer

**Summary:**

The statement “Diagonals of a rhombus are equal and perpendicular to each other” is false

**☛ Related Questions:**

- Three angles of a quadrilateral ABCD are equal. Is it a parallelogram? Why or why not
- Diagonals AC and BD of a quadrilateral ABCD intersect each other at O such that OA : OC = 3: 2. Is A . . . .
- Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, d . . . .

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