State whether the following statement is true or false:
The diagonals of a rhombus bisect each other at right angles.

In trapezium $ABCD$,$AB || CD$. Points $P$ and $Q$ are the midpoints of $AD$ and $BC$ respectively. If $AB = 18 \, cm$ and $PQ = 15 \, cm$,then $CD = \dots \, cm$.

In the given figure,$AX$ and $CY$ are respectively the bisectors of the opposite angles $A$ and $C$ of a parallelogram $ABCD$. Show that $AX \parallel CY$.

$ABCD$ is a rhombus in which the altitude from $D$ to side $AB$ bisects $AB$. Find the angles of the rhombus.

Diagonals of a parallelogram $ABCD$ intersect at $O.$ If $\angle BOC = 90^{\circ}$ and $\angle BDC = 50^{\circ},$ then $\angle OAB$ is (in $^{\circ}$)

Three angles of a quadrilateral are $75^{\circ}, 90^{\circ}$ and $75^{\circ}$. The fourth angle is (in $^{\circ}$)