(A) We know that the diagonals of a parallelogram bisect each other at their point of intersection.Since $O$ is the intersection point,$AC = 2 \times

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(A) We know that the diagonals of a parallelogram bisect each other at their point of intersection.Since $O$ is the intersection point,$AC = 2 \times OA$ and $BD = 2 \times OD$.Given $OA = 3\, cm$ and $OD = 2\, cm$.Therefore,$AC = 2 \times 3\, cm = 6\, cm$.And $BD = 2 \times 2\, cm = 4\, cm$.Hence,the lengths of $AC$ and $BD$ are $6\, cm$ and $4\, cm$ respectively.

Class 9 Mathematics Quadrilaterals Mix Examples - Quadrilaterals

Medium

Diagonals $AC$ and $BD$ of a parallelogram $ABCD$ intersect each other at $O$. If $OA = 3\, cm$ and $OD = 2\, cm$,determine the lengths of $AC$ and $BD$.

A
$AC = 6\, cm, BD = 4\, cm$
B
$AC = 3\, cm, BD = 2\, cm$
C
$AC = 4\, cm, BD = 6\, cm$
D
$AC = 5\, cm, BD = 5\, cm$

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Mix Examples - Quadrilaterals

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$(1)$ If no three points out of four coplanar points are collinear,then a $\ldots \ldots \ldots$ figure formed by joining these four points in order is called a quadrilateral.
$(2)$ $A$ quadrilateral has $\ldots \ldots \ldots$ pairs of opposite sides.

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Diagonals $AC$ and $BD$ of a parallelogram $ABCD$ intersect each other at $O$. If $OA = 3\, cm$ and $OD = 2\, cm$,determine the lengths of $AC$ and $BD$.

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In trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 80^{\circ}$ and $\angle B = 75^{\circ}$,then find $\angle D$. (in $^{\circ}$)

$P, Q, R$ and $S$ are respectively the mid-points of the sides $AB, BC, CD$ and $DA$ of a quadrilateral $ABCD$ such that $AC \perp BD$. Prove that $PQRS$ is a rectangle.

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$(1)$ If no three points out of four coplanar points are collinear,then a $\ldots \ldots \ldots$ figure formed by joining these four points in order is called a quadrilateral.
$(2)$ $A$ quadrilateral has $\ldots \ldots \ldots$ pairs of opposite sides.