Heather is given the coordinates of the vertices of quadrilateral

Question

ABCD.
ABCD.
She is asked to prove whether the quadrilateral is a parallelogram. Her proof follows the diagram.

Given:

Quadrilateral
ABCD
ABCD
has vertices at
A(−8,−1),
A(−8,−1),
B(−1,−7),
B(−1,−7),
C(2,2),
C(2,2),
and
D(−5,8).
D(−5,8).

Prove:

Quadrilateral
ABCD
ABCD
is a parallelogram

Answer 1

check each side length
there should be two pairs of equal length
check each side's slope
there should be two pairs that are the same