In quadrilateral $ABCD$,$\angle A = 100^{\circ}$,$\angle B = 80^{\circ}$,and $\angle C = 120^{\circ}$. Find $\angle D$. (in $^{\circ}$)

Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.

$E$ and $F$ are respectively the mid-points of the non-parallel sides $AD$ and $BC$ of a trapezium $ABCD$. Prove that $EF \parallel AB$ and $EF = \frac{1}{2}(AB + CD)$.

In a parallelogram $ABCD$,$AB = 10 \, cm$ and $AD = 6 \, cm$. The bisector of $\angle A$ meets $DC$ in $E$. $AE$ and $BC$ produced meet at $F$. Find the length of $CF$ (in $cm$).

$P$ and $Q$ are points on opposite sides $AD$ and $BC$ of a parallelogram $ABCD$ such that $PQ$ passes through the point of intersection $O$ of its diagonals $AC$ and $BD$. Show that $PQ$ is bisected at $O$.

Perimeter of rectangle $PQRS$ is $40\, cm$. If $PQ : QR = 3 : 5$,then $RS = \ldots \ldots \ldots \, cm$.