This is a parallelogram. Two pairs of parallel and congruent sides
1) By definition a Parallelogram is a quadrilateral with two pairs of parallel and congruent sides.
2) So let's plug into the distance formula the following coordinates:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Let's find the distance of line segment LE, L(-3,1), E(2,6):
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(2_{}-(-3)_{})^2+(6_{}-1_{})^2} \\ d_{LE}=5\sqrt[]{2} \end{gathered}[/tex]Similarly now let's focus on the side EA whose points are E (2,6), A(9,5)
[tex]d=\sqrt[]{(9-2_{})^2+(5-6_{})^2}=5\sqrt[]{2}[/tex]Now we can deal with the side AP, A(9,5) and P(4,0):
[tex]\begin{gathered} d_{AP}=\sqrt[]{(4-9)^2+(0-5)^2}=5\sqrt[]{2} \\ \end{gathered}[/tex]And finally, let's check side PL, P(4,0) and L(-3,1)
[tex]d_{PL}=\sqrt[]{(-3-4)^2+(1-0)^2}=5\sqrt[]{2}[/tex]3) Hence, we can conclude that the four sides are congruent and there are two sides parallel, and therefore this is a parallelogram. Note that in this case, this parallelogram could be labeled as a rhombus as well.