In a rhombus $ABCD$,if $AB = 13 \text{ cm}$,then the perimeter of $ABCD = \ldots \ldots \ldots \text{ cm}$.

In parallelogram $ABCD$,$\angle A = \angle B + 50^{\circ}$. Find the measure of each angle of the quadrilateral $ABCD$.

In the figure,$AB \parallel DE$,$AB = DE$,$AC \parallel DF$ and $AC = DF$. Prove that $BC \parallel EF$ and $BC = EF$.

The figure formed by joining the mid-points of the sides of a quadrilateral $ABCD,$ taken in order,is a square only if,

Prove that the line segment joining the midpoints of the diagonals of a trapezium is parallel to the parallel sides of the trapezium and is equal to half the difference of the lengths of the parallel sides.

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 $CD = \dots \, cm$.