Question

For every 10 yards on a football field, there is a boldly marked line labeled with the amount of yards. Each of those lines is perpendicular to both sidelines. What can be said about the relationship of the sidelines? Justify your answer.

a. The sidelines are perpendicular to each other by the definition of the Transitive Property.

b. The sidelines are parallel by the Same-Side Interior Angles Theorem.

c. The sidelines are perpendicular by the Perpendicular Transversal Theorem

d. The sidelines are parallel because they are perpendicular to the same line.

Answer 1

The sidelines are perpendicular by the Perpendicular Transversal Theorem.

Step-by-step explanation:

The correct answer is c. The sidelines are perpendicular by the Perpendicular Transversal Theorem.

The Perpendicular Transversal Theorem states that if a transversal intersects two parallel lines, then the alternate interior angles are congruent. In this case, the boldly marked lines labeled with the amount of yards are transversals intersecting the sidelines, which are believed to be parallel. Therefore, the lines must be perpendicular to each other based on this theorem.

For example, if we have two sidelines that are parallel to each other, and a transversal (the boldly marked line) intersects the sidelines, the alternate interior angles formed will be congruent. This confirms the perpendicular relationship between the sidelines.

Answer 2

The sidelines are parallel to one another, because
they are perpendicular to the same line.