A quadrilateral is a parallelogram if both pairs of opposite sides are parallel.
Parallel
A pair of lines are parallel if they have the same slope. Let's check if the sides are parallel. We will start by the pair QT and RS.
Side
Slope Formula
Simplify
Slope of QT: ( -5,2), ( - 1,6)
6- 2/- 1-( - 5)
4/4
Slope of RS: ( -3, -6), ( 2, 2)
2-( -6)/2-( -3)
8/5
The slopes of QT and RS are not equal, so these sides are not parallel. Let's now check the pair QR and TS.
Side
Slope Formula
Simplify
Slope of QR: ( -5,2), ( -3, -6)
- 3- 2/- 6-( - 5)
-5/1
Slope of TS: ( - 1,6), ( 2, 2)
2- 6/2-( -1)
-4/3
The slopes of QR and TS are not equal, so these sides are also not parallel. The slopes of the opposite sides of our quadrilateral are not equal. Therefore, both pairs of opposite sides are not parallel. Our quadrilateral is not a parallelogram.
