Question

Lydia is trying to prove that a quadrilateral in a coordinate plane is a square. First, she uses the slope formula to prove that there are two pairs of parallel sides. Next, she uses the distance formula to prove that all sides are equal. What additional step must Lydia perform before reaching a conclusion that the quadrilateral is a square?

Answer 1

To be classified as a square, a quadrilateral must have 2 pairs of parallel sides, 4 sides equal in length, and 4 right angles. By using the slope formula, it can be determined whether the quadrilateral's sides are perpendicular. If so, 4 right angles exist and the shape is a square. If not, the shape is not a square.

Answer 2

Answer: Use the slope formula to prove that four right angles exist as a result of perpendicular sides.

Explanation:

To be classified as a square, a quadrilateral must have 2 pairs of parallel sides, 4 sides equal in length, and 4 right angles. By using the slope formula, it can be determined whether the quadrilateral's sides are perpendicular. If so, 4 right angles exist and the shape is a square. If not, the shape is not a square.