Question

2 multiple choice 5 points
consider the diagram.
given that $r\parallel s$ and $q$ is a transversal, we know that $\angle3\cong\angle6$ by the ______.
corresponding angles theorem
alternate interior angles theorem
vertical angles theorem
alternate exterior angles theorem

Explanation:

1. Identify the position of $\angle 3$ and $\angle 6$: Both angles lie between the parallel lines $r$ and $s$, on opposite sides of the transversal $q$.
2. Match the angle pair to the theorem: Angles that are inside the parallel lines and on alternate sides of the transversal are defined as alternate interior angles, and the Alternate Interior Angles Theorem states these angles are congruent when the lines are parallel.

Answer:

Alternate Interior Angles Theorem