$(1)$ $A$ quadrilateral in which only one pair of opposite sides are parallel is a $\ldots \ldots \ldots$.
$(2)$ The diagonals of a rectangle are $\ldots \ldots \ldots$.

$AC$ is one of the diagonals of quadrilateral $ABCD$. $BM$ and $DN$ are altitudes on $AC$ from $B$ and $D$ respectively. If $AC = 18 \, cm$,$BM = 10 \, cm$,and $DN = 6 \, cm$,then $ar(ABCD) = \dots \dots \, cm^2$.

$AB$ and $CD$ are respectively the smallest and longest sides of a quadrilateral $ABCD$ (see Fig). Show that $\angle A > \angle C$ and $\angle B > \angle D$.

In square $ABCD$,$AC = 16 \text{ cm}$,then $\operatorname{ar}(ABCD) = \dots \text{ cm}^2$.

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

Prove that in a parallelogram,the bisectors of any two consecutive angles intersect at right angles.