$\mathrm{A}(8,-6),\mathrm{B}(-4,2)$ and $\mathrm{C}(0,-10)$ are vertices of a triangle $\mathrm{ABC}$. If $\mathrm{P}$ is the midpoint of $\mathrm{AB}$ and $\mathrm{Q}$ is the mid-point of $\mathrm{AC}$, use co-ordinate geometry to show that $\mathrm{PQ}$ is parallel to $\mathrm{BC}$. Give a special name to quadrilateral $\mathrm{PBCQ}$.

The given figure (not drawn to scale) shows two straight lines $\mathrm{AB}$ and $\mathrm{CD}$. If equation of the line $\mathrm{AB}$ is :
$y=x+1$ and equation of line $\mathrm{CD}$ is $y=\sqrt{3}x-1$. Write down the inclination of lines $\mathrm{AB}$ and $\mathrm{CD}$ also, find the angle $\theta$ between $\mathrm{AB}$ and $\mathrm{CD}$.