Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.

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

In the given figure, $\mathrm{ABCD}$ and $\mathrm{AEFG}$ are two parallelograms.

If $\angle \mathrm{C}=55°$ and $\angle \mathrm{F}=k°$, then find the value of $k$.

Opposite angles of a quadrilateral $\mathrm{ABCD}$ are equal. If $\mathrm{AB}=4 \mathrm{cm}$ and $\mathrm{CD}=x \mathrm{cm}$, then find the value of $x$.