The diagonals of a rhombus are $16\,cm$ and $30\,cm$. Find its perimeter. (in $,cm$)

In the given figure,it is given that $BDEF$ and $FDCE$ are parallelograms. Can you say that $BD = CD$? Why or why not?

$PQ$ and $RS$ are two equal and parallel line segments. Any point $M$ not lying on $PQ$ or $RS$ is joined to $Q$ and $S$. Lines are drawn through $P$ parallel to $QM$ and through $R$ parallel to $SM$,meeting at $N$. Prove that line segments $MN$ and $PQ$ are equal and parallel to each other.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Write True or False and justify your answer:
$ABCD$ is a parallelogram and $X$ is the mid-point of $AB$. If $\text{ar}(AXCD) = 24 \text{ cm}^2$,then $\text{ar}(ABC) = 24 \text{ cm}^2$.

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