Answer:
DOGS is a parallelogram.
Explanation:
Given the quadrilateral DOGS with coordinates D(1, 1), O(2, 4), G(5, 6), and S(4,3).
To prove that it is a parallelogram, we need to show that the opposite lengths are equal. That is:
Using the Distance Formula

For D(1, 1) and O(2, 4)

For G(5, 6), and S(4,3).

For O(2, 4) and G(5, 6)

For S(4,3) and D(1, 1)

Since:
Then, quadrilateral DOGS is a parallelogram.