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
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• Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, d . . . .