Question

consider the diagram.
given that ( r parallel s ) and ( q ) is a transversal, we know that ( angle 3 cong angle 6 ) by the ______.

• corresponding angles theorem
• alternate interior angles theorem
• vertical angles theorem
• alternate exterior angles theorem

Explanation:

∠3 and ∠6 lie between the parallel lines \(r \parallel s\) and on opposite sides of the transversal \(q\). This matches the definition of alternate interior angles, and the theorem states such angles are congruent for parallel lines cut by a transversal.

Answer:

alternate interior angles theorem