Question

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

Explanation:

• Corresponding angles theorem: Angles in matching positions. Not the case for \(\angle3\) and \(\angle6\).
• Alternate interior angles theorem: When two parallel lines are cut by a transversal, the alternate interior angles are congruent. \(\angle3\) and \(\angle6\) lie between the parallel lines \(r\) and \(s\) and on opposite sides of the transversal \(q\).
• Vertical angles theorem: Angles opposite each other when two lines intersect. Not relevant here.
• Alternate exterior angles theorem: Angles outside the parallel lines. Not for \(\angle3\) and \(\angle6\).

Answer:

alternate interior angles theorem