Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Quadrilaterals, Exercise 2: Exercise 8.2

Diagonals $AC$ and $BD$ of a quadrilateral intersect each other at $O$ such that $OA:OC=3:2$. Is $ABCD$ a parallelogram? Why or why not?

Justify your answer for the following statements.

$ABCD$ is a parallelogram. If its diagonals are equal, then find the value of $\angle ABC$.

In the given figure, $ABCD$ is a parallelogram. $E$ and $F$ are points on opposite sides $AD$ and $BC$, respectively, such that $ED=\frac{1}{3}AD$ and $BF=\frac{1}{3}BC$.

If $\angle ADF=60°$, then find $\angle BFD$.

$ABCD$ is a trapezium in which $AB\Vert DC$ and $\angle A=\angle B=55°$. Find $\angle C$ and $\angle D$ of a trapezium.

If angles $A, B, C$ and $D$ of the quadrilateral $ABCD$, taken in order are in the ratio $3:7:6:4$, then show that $ABCD$ is a trapezium.

The diagonals of a rectangle $ABCD$ intersect at a point $O$. If $\angle COD=78°$, then find the value of $\angle OAB$.

In a quadrilateral $ABCD, \angle B=130°, \angle C=60°$ and angle bisectors of $\angle A$ and $\angle D$ meet at $P$. Find $\angle APD$.

In the given figure, $PQRS$ is a parallelogram in which $PQ$ is produced to $T$, such that $QT=PQ$. Prove that $ST$ bisects $RQ$.