Explain how $DEAR$ is a trapezium. Which of its two sides are parallel? 

$BASE$ is a rectangle. Its diagonals intersect at $O$. Find $x$, if $OB=5x+1$ and $OE=2x+4$.

Is quadrilateral $ABCD$ a parallelogram, if $\angle A=70°$ and $\angle C=65°$? Give reason. 

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.

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

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