Question

consider the diagram.
given that r||s and q is a transversal, we know that
∠3 ≅∠6 by the ______.
corresponding angles theorem
alternate interior angles theorem
vertical angles theorem
alternate exterior angles theorem

Explanation:

To determine the theorem for \(\angle 3 \cong \angle 6\) with \(r \parallel s\) and transversal \(q\):

• Alternate Interior Angles Theorem: When two parallel lines are cut by a transversal, alternate interior angles (angles between the lines, on opposite sides of the transversal) are congruent.
• \(\angle 3\) and \(\angle 6\) lie between lines \(r\) and \(s\) (interior) and on opposite sides of transversal \(q\) (alternate), so they are alternate interior angles.
• Other options: Corresponding angles are in the same position; vertical angles are opposite each other (not related to parallel lines here); alternate exterior angles are outside the lines.

Answer:

B. alternate interior angles theorem