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?
(B) quadrilateral is a parallelogram if and only if its diagonals bisect each other,meaning $OA = OC$ and $OB = OD$.
In the given quadrilateral $ABCD$,the ratio of the segments of the diagonal $AC$ is $OA : OC = 3 : 2$.
Since $OA \neq OC$,the diagonals do not bisect each other.
Therefore,$ABCD$ is not a parallelogram.
In the given quadrilateral $ABCD$,the ratio of the segments of the diagonal $AC$ is $OA : OC = 3 : 2$.
Since $OA \neq OC$,the diagonals do not bisect each other.
Therefore,$ABCD$ is not a parallelogram.
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