Question

point of intersection of diagonals of a quadrilateral divides one of the diagonals in the ratio 11 gm .Can it be a parallelogram ? Justify.​

Answer 1

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Let ABCD be the quadrilateral in which AC and BD are the diagonals that intersect at O.

Now, AO/OC = 1/2

We know that diagonals of a parallelogram bisect eah other.

So, for ABCD to be a parallelogram,

AO/OC = 11

But here AO/OC = 1/2.

So, the quadrilateral can't be a parallelogram in which point of intersection of the diagonals divide one diagonalin the ratio of 1 : 2.

Let ABCD be the quadrilateral in which AC and BD are the diagonals that intersect at O.

Now, AO/OC = 1/2

We know that diagonals of a parallelogram bisect eah other.

So, for ABCD to be a parallelogram,

AO/OC = 11

But here AO/OC = 1/2.

So, the quadrilateral can't be a parallelogram in which point of intersection of the diagonals divide one diagonalin the ratio of 1 : 2.

Answer 2

Step-by-step explanation:

Let ABCD be the quadrilateral in which AC and BD are the diagonals that intersect at O.

Now,

AO /OC =1 /2

We know that diagonals of a parallelogram bisect eah other.

So, for ABCD to be a parallelogram,

AO /OC= 1 / 1

But here

AO /OC= 1 /2

So, the quadrilateral can 't be a parallelogram in which point of intersection of the diagonals divide one diagonal in the ratio of 1 : 2.

ANSWER= NO