Two adjacent sides of a parallelogram are in the ratio $5:3$ and the perimeter of the parallelogram is $48 \mathrm{cm}$. Find the length of each of its sides. 

The diagonals of the quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Draw a rough figure to justify your answer. 

$ABCD$ is a trapezium in which $AB\parallel DC$. If $\angle A=\angle B=30°$, what are the measures of the other two angles? 

Name the parallelogram in which two adjacent sides are equal.

A parallelogram in which one angle is $90°$ and two adjacent sides are equal is a _____.

In trapezium $ABCD, AB\parallel DC$.·If $\angle D=x°$ and $\angle A=k°-x°$ then $k=$_____.

Every diagonal in a parallelogram divides it into _____ congruent triangles. 

In parallelogram $ABCD$, its diagonals $AC$ and $BD$ intersect at $O$. If $AO=5 \mathrm{cm}$ then $AC=$ _____ $\mathrm{cm}$. 

In a rhombus $ABCD$, its diagonals intersect at '$O$'. Then $\angle AOB=$ _____ degrees.