In parallelogram $PQRS$,$PQ = 8 \, \text{cm}$ and $QR = 5 \, \text{cm}$,then the perimeter of $PQRS = \ldots \ldots \ldots$ (in $, \text{cm}$)

$P$ and $Q$ are the mid-points of the opposite sides $AB$ and $CD$ of a parallelogram $ABCD.$ $AQ$ intersects $DP$ at $S$ and $BQ$ intersects $CP$ at $R.$ Show that $PRQS$ is a parallelogram.

Two parallel lines are intersected by a transversal. Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

In rhombus $ABCD$,$\angle A = \angle B - 30^{\circ}$,then $\angle C = \ldots$ (in $^{\circ}$)

Which of the following is not true for a parallelogram?

In parallelogram $ABCD$,the diagonals intersect at $P$. If $PA = 3.8 \, cm$ and $PB = 5.2 \, cm$,then $BD = \dots \dots \dots cm$.