(a) If AB = CD and AB || CD then ABCD is a parallelogram.
[tex]A(3,0), B(4,3), C(7,3), D(6,0)
\\d(A,B)= \sqrt{(4-3)^2+(3-0)^2} = \sqrt{10}
\\d(C,D)= \sqrt{(6-7)^2+(0-3)^2} = \sqrt{10}
\\AB=CD
\\
\\m_{AB}= \frac{3-0}{4-3} =
\\
\\m_{CD}= \frac{0-3}{6-7}=3
\\
\\m_{AB}=m_{CD}\Rightarrow AB||CD [/tex]
(b) If AB ≠ BC then ABCD is not a rhombus.
[tex]B(4,3), C(7,3)
\\d(B,C)= \sqrt{(7-4)^2+(3-3)^2}=3
\\BC \neq AB [/tex]
