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;

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

Explanation;

According to the perpendicular Transversal Theorem, In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line also. Additionally, the converse perpendicular transversal theorem states that, in a plane, if two lines are perpendicular to the same line, then they are parallel. Thus, the sidelines are parallel and also perpendicular to the same line.

The correct answer is:

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

Explanation:

Since the 10 yard lines are perpendicular to both sidelines, this means they are congruent. We have a line (transversal) perpendicular to two other lines, cutting them so that the angles on one side of the transversal inside the lines are congruent. These would be considered Same-Side Interior Angles (since they are on the same side of the transversal and inside the lines), which means the sidelines are parallel by the Same-Side Interior Angles theorem.