A quadrilateral is a parallelogram if both pairs of opposite sides are congruent. Let's check if the sides are congruent. We start by the pair AB and CD.
Side
Distance Formula
Simplify
Length of AB: ( - 6,- 5), ( - 1,- 4)
sqrt(( - 1-( - 6))^2+( - 4-( - 5))^2)
sqrt(26)
Length of CD: ( 0, -1), ( - 5, - 2)
sqrt(( - 5-( 0))^2+( - 2-( -1))^2)
sqrt(26)
The lengths of the sides are equal, so AB and CD are congruent. Now let's check the pair AD and BC.
Side
Distance Formula
Simplify
Length of AD: ( - 6,- 5), ( - 5, - 2)
sqrt(( - 5-( - 6))^2+( - 2-( - 5))^2)
sqrt(10)
Length of BC: ( - 1,- 4), ( 0, -1)
sqrt(( 0-( - 1))^2+( - 1-( - 4))^2)
sqrt(10)
The lengths of the sides are equal, so AD and BC are also congruent. Both pairs of opposite sides are congruent. Therefore, the given quadrilateral is a parallelogram.
