Question

select the correct answer.
transversal t cuts parallel lines r and s as shown in the diagram. which theorem does the diagram illustrate?
a. alternate interior angles theorem
b. alternate exterior angles theorem
c. same - side interior angles theorem
d. corresponding angles theorem

Explanation:

• Alternate Interior Angles Theorem: When a transversal cuts two parallel lines, alternate interior angles (angles that lie between the two parallel lines and on opposite sides of the transversal) are congruent. In the given diagram, the two marked angles are between the parallel lines \(r\) and \(s\) and on opposite sides of the transversal \(t\).
• Alternate Exterior Angles Theorem: Deals with angles outside the parallel lines. The marked angles in the diagram are not exterior angles.
• Same - Side Interior Angles Theorem: States that same - side interior angles (angles between the parallel lines and on the same side of the transversal) are supplementary. The marked angles are not on the same side.
• Corresponding Angles Theorem: Corresponding angles are in the same relative position (e.g., both above the parallel lines and on the same side of the transversal). The marked angles do not have a corresponding position relationship.

Answer:

A. Alternate Interior Angles Theorem