The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1:2. Can it be a parallelogram? Why or why not?

Solution:

Given, the point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1:2.

We have to determine if the quadrilateral is a parallelogram or not.

Let us consider a quadrilateral ABCD.

Let AC and BD be the diagonals that intersect at O.

Now, OC/AO = 2/1

We know that diagonals of a parallelogram bisect each other i.e.,the diagonals of a parallelogram intersect each other in the ratio 1 : 1.

So, OC/AO = 1/2

Given, OC/AO = 2/1

Therefore, the quadrilateral can't be a parallelogram since the point of intersection of the diagonals divides one diagonal in the ratio of 1:2.

✦ Try This: The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 3:2. Can it be a Rhombus? Why or why not

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 139

The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1:2. Can it be a parallelogram? Why or why not

Summary:

The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1:2. It cannot be a parallelogram since the point of intersection of the diagonals divides one diagonal in the ratio of 1:2.

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