A quadrilateral is a parallelogram if both pairs of opposite sides are parallel. Let's check if the sides are parallel.
Side
Slope Formula
Simplify
Slope of AD: ( -3,4), ( - 2,- 2)
- 2- 4/- 2-( - 3)
- 6
Slope of BC: ( 4,5), ( 5, -1)
-1- 5/5- 4
- 6
Slope of AB: ( -3,4), ( 4,5)
5- 4/4-( - 3)
1/7
Slope of DC: ( - 2, - 2), ( 5, -1)
-1-( - 2)/5-( - 2)
1/7
The slopes of the opposite sides of our quadrilateral are equal. Therefore, both pairs of opposite sides are parallel. Our quadrilateral is a parallelogram.
