Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.

Solution:

Consider a parallelogram

AC and BD are the diagonals

It intersects each other at the point O

The properties of a parallelogram are

a. The opposite sides of a parallelogram are parallel.

b. The opposite sides of a parallelogram are equal.

c. The opposite angles of a parallelogram are equal.

d. The diagonals of a parallelogram bisect each other.

e. Same-side interior angles supplement each other.

f. The diagonals divide the parallelogram into two congruent triangles.

We know that

Diagonals of a parallelogram bisect each other but not at 90°.

So the diagonals are not perpendicular

Therefore, the statement is false.

✦ Try This: Diagonals EG and FH of a parallelogram EFGH intersect each other at O. If OE = 6 cm and OH = 5 cm, determine the lengths of EG and FH.

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

NCERT Exemplar Class 9 Maths Exercise 8.2 Problem 2

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer

Summary:

The statement “Diagonals of a parallelogram are perpendicular to each other” is false as the diagonals bisect each other but not at 90°

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