$\mathrm{ABCD}$ is a rectangle in which diagonal $\mathrm{AC}$ bisects $\angle \mathrm{A}$ as well as $\angle \mathrm{C}$. Show that diagonal $BD$ bisects $\angle \mathrm{B}$ as well as $\angle \mathrm{D}$.

In the following figure, through $A, B$ and $C$, lines $RQ, PR$ and $QP$ have been drawn respectively parallel to sides $BC, CA$ and $\mathrm{AB}$ of a triangle $\mathrm{ABC}$. Show that $\mathrm{BC}=\frac{1}{2}\mathrm{RQ}$.

In the figure given below, $D, E$ and $F$ are mid-points of the sides $BC$, $\mathrm{CA}$ and $\mathrm{AB}$, respectively of $∆\mathrm{ABC}$. $\mathrm{AB}=6 \mathrm{cm}, \mathrm{BC}=4.8 \mathrm{cm}$ and $\mathrm{CA}=5.6 \mathrm{cm}$. If the perimeter of the trapezium $FBCE$ is $k \mathrm{cm}$, find $k$.

In the figure given below, $D, E$ and $F$ are mid-points of the sides $BC$, $\mathrm{CA}$ and $\mathrm{AB}$ respectively of $∆\mathrm{ABC}$. $\mathrm{AB}=6 \mathrm{cm}, \mathrm{BC}=4.8 \mathrm{cm}$ and $\mathrm{CA}=5.6 \mathrm{cm}$. If the perimeter of the triangle $DEF$ is $k \mathrm{cm}$, find $k$.