In parallelogram $ABCD$,$AB = 12.5 \, cm$ and $BC = 7 \, cm$,then find the perimeter of $ABCD$ in $cm$.

In parallelogram $XYZW$,$XY = 24 \, cm$. Altitudes $WP$ and $WQ$ are corresponding to bases $XY$ and $YZ$ respectively. If $WP = 6 \, cm$ and $WQ = 8 \, cm$,then find $YZ$ and the perimeter of parallelogram $XYZW$.

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

In parallelogram $ABCD$,two points $P$ and $Q$ are taken on diagonal $BD$ such that $DP = BQ$ (see Fig). Show that: $AP = CQ$.

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 $PQRS$.

Diagonal $AC$ of a parallelogram $ABCD$ bisects $\angle A$ (see Fig). Show that it bisects $\angle C$ also.