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
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Explanation:

Step1: Recall the definitions of different angle theorems

• Corresponding angles: Angles in the same relative position.
• Alternate interior angles: Angles between the two parallel lines and on opposite sides of the transversal.
• Vertical angles: Opposite angles formed by two intersecting lines.
• Alternate exterior angles: Angles outside the two parallel lines and on opposite sides of the transversal.

Step2: Analyze the position of ∠3 and ∠6

∠3 and ∠6 are between the parallel lines \(r\) and \(s\) and on opposite sides of the transversal \(q\).

Answer:

alternate interior angles theorem