R K Bansal Solutions for Exercise 1: EXERCISE

The following figure shows a trapezium $ABCD$ in which $AB$ is parallel to $DC$ and $AD=BC$. Prove that: $\angle DAB=\angle CBA$.

The following figure shows a trapezium $ABCD$ in which $AB$ is parallel to $DC$ and $AD=BC$. Prove that: $\angle ADC=\angle BCD$.

The following figure shows a trapezium $ABCD$ in which $AB$ is parallel to $DC$ and $AD=BC$. Prove that: $AC=BD$.

The following figure shows a trapezium $ABCD$ in which $AB$ is parallel to $DC$ and $AD=BC$. Prove that: $OA=OB \text{and} OC=OD$.

In the given figure, $AP$ is a bisector of $\angle A$ and $CQ$ is bisector of $\angle C$ of parallelogram $ABCD$. Prove that $APCQ$ is a parallelogram.

In case of a parallelogram prove that: the bisectors of any two adjacent angles intersect at $90°$

In case of a parallelogram prove that: the bisectors of opposite angles are parallel to each other.

In the following figure, $ABCD$ and $PQRS$ are two parallelograms such that $\angle D=120°$ and $\angle Q=70°$. Find the value of $x$.