Step-by-step explanation:
To prove that two sides are parallel on a graph, we must show that their slopes are the same. Plotting this on Desmos, we get the first image attached. Finding the slopes of each line, we get
[tex]TOP\\\frac{5-3}{6-1} =2/5\\BOTTOM\\\frac{-1-(-1)}{7-2} =2/5\\RIGHT\\-4\\LEFT\\-4[/tex]
As the top slope is the same as the bottom, and the right is the same as the left, this is a parallelogram.
To prove that two sides are congruent, we must find their lengths. The distance formula is
[tex]\sqrt(x_{1}+x_{2})^2+(y_{1}+y_{2})^2 } \\[/tex]
Finding the distances, we get
TOP: [tex]\sqrt{29}[/tex]
BOTTOM: [tex]\sqrt{29}[/tex]
RIGHT:[tex]\sqrt{17}[/tex]
LEFT:[tex]\sqrt{17}[/tex]
As the lengths are the same, the sides are congruent
