1. Prove that quadrilateral DOGS is

a parallelogram. The coordinates

of DOGS are D(1, 1), (2, 4),

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

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DOGS is a parallelogram.

Step-by-step 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.

correct answers below: