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.
Explore More
Similar Questions
In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $BC = 8.2 \text{ cm}$,then $PQ = \dots \text{ cm}$.
Medium
View SolutionIn $\Delta ABC$,$AD$ is a median and $E$ is the midpoint of $AD$. $BE$ is extended to intersect $AC$ at $F$. Prove that $AF = \frac{1}{3} AC$.
Medium
View Solution$XYZW$ is a rhombus. If the diagonals $XZ$ and $YW$ intersect at $P$,then $\angle XPY = \ldots \ldots \ldots$ (in $^o$)
Medium
View Solution$D$ and $E$ are the mid-points of the sides $AB$ and $AC$ respectively of $\triangle ABC$. $DE$ is produced to $F$. To prove that $CF$ is equal and parallel to $DA$,we need an additional information which is
Easy
View SolutionIn $\triangle ABC$,$AB = 5\, cm$,$BC = 8\, cm$,and $CA = 7\, cm$. If $D$ and $E$ are respectively the mid-points of $AB$ and $BC$,determine the length of $DE$. (in $, cm$)
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo