EXERCISE 10B

In the figure given below, $ABCD$ is a rectangle. Find the values of $x°$ and $y°$ in each case.

In the figure given below, $ABCD$ is a rectangle. Find the values of $x°$ and $y°$ in each case.

In a rhombus $ABCD,$ the altitude from $D$ to the side $AB$ bisects $AB$. Find the angles of the rhombus.

In a rhombus $ABCD$ show that diagonal $AC$ bisects $\angle A$ as well as $\angle C$ and diagonal $BD$ bisects $\angle B$ as well as $\angle \mathrm{D}$

In a parallelogram $ABCD$, points $M$ and $N$ have been taken on opposite sides $AB$ and $CD$ respectively such that $AM=CN$. Show that $AC$ and $MN$ bisect each other.

In the adjoining figure, $ABCD$ is a parallelogram. If $P$ and $Q$ are points on $AD$ and $BC$ respectively such that $AP=\frac{1}{3}AD$ and $CQ=\frac{1}{3}BC$, prove that $AQCP$ is a parallelogram.

In the adjoining figure, $ABCD$ is a parallelogram whose diagonals intersect each other at $O.$ A line segment $EOF$ is drawn to meet $AB$ at $E$ and $DC$ at $F.$ Prove that $OE=OF$.

The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is $60°.$ Find the angles of the parallelogram.