Diagonals AC and BD of a quadrilateral ABCD intersect each other at O such that OA : OC = 3: 2. Is ABCD a parallelogram? Why or why not?

Solution:

In a parallelogram ABCD

It is given that

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.

As OA: OC = 3: 2 is not equal

ABCD is not a parallelogram

Therefore, ABCD is not a parallelogram as OA is not equal to OC.

✦ Try This: Diagonals PR and QS of a quadrilateral PQRS intersect each other at O such that OP : OR = 5: 3. Is PQRS a parallelogram? Why or why not?

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

NCERT Exemplar Class 9 Maths Exercise 8.2 Sample Problem 4

Diagonals AC and BD of a quadrilateral ABCD intersect each other at O such that OA : OC = 3: 2. Is ABCD a parallelogram? Why or why not

Summary:

If diagonals AC and BD of a quadrilateral ABCD intersect each other at O such that OA : OC = 3: 2, ABCD is not a parallelogram

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