On graph paper, plot and connect the points $A(1,1)$, $B(2,3)$, $C(5,3)$, and $D(4,1)$ to form quadrilateral $ABCD$.  

1. What is the best name for quadrilateral $ABCD$? Justify your answer.

   Hint (a):

   Explain why it is not a rhombus.

   Answer (a):

   $ABCD$ is a parallelogram because opposite sides are parallel.

2. Find and compare $m∠DAB$ and $m∠BCD$. What is their relationship?

3. Find the equations of diagonals $\overline{AC}$ and $\ \overline{BD}$. Are the diagonals perpendicular?

   Hint (c):

   Find the slope of each diagonal.

4. Find the point where diagonals $\overline{AC}$ and $\ \overline{BD}$ intersect.