Answer
See explanations.
Work Step by Step
We need to show that the opposite sides are parallel.
Step 1. Let A, B, C, D be the vertices $A(1,-1),B(4,1),C(2,2),D(5,4)$
Step 2. Find slopes of each side: $m_{AB}=\frac{-1-1}{1-4}=\frac{2}{3}$, $m_{CD}=\frac{4-2}{5-2}=\frac{2}{3}$, $m_{AC}=\frac{-1-2}{1-2}=3$, $m_{BD}=\frac{4-1}{5-4}=3$,
Step 3. Since $AB\parallel CD$ and $AC\parallel BD$, we have a parallelogram.
