Which of the following is not true for a parallelogram?

Show that the diagonals of a rhombus are perpendicular to each other.

$ABCD$ is a rhombus. Show that diagonal $AC$ bisects $\angle A$ as well as $\angle C$ and diagonal $BD$ bisects $\angle B$ as well as $\angle D$.

$ABCD$ is a parallelogram in which $P$ and $Q$ are mid-points of opposite sides $AB$ and $CD$ respectively. If $AQ$ intersects $DP$ at $S$ and $BQ$ intersects $CP$ at $R$,show that: $APCQ$ is a parallelogram.

$A$ diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

In parallelogram $PQRS$,$PQ = 15 \, cm$. Altitudes $SM$ and $SN$ are corresponding to bases $PQ$ and $QR$ respectively. If $SM = 6 \, cm$ and $SN = 10 \, cm$,find $QR$ and the perimeter of $PQRS$.