Question

semester t1c geometry with statistics schoangles and lines
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

Explanation:

Step1: Recall Angle Theorems

Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then alternate interior angles are congruent. Corresponding Angles Theorem: If two parallel lines are cut by a transversal, corresponding angles are congruent.

Step2: Identify Angle Positions

∠3 and ∠6: Line \( r \parallel s \), transversal \( q \). ∠3 is between \( r, s \) (interior) and on opposite sides of transversal (alternate). ∠6 is also interior, alternate to ∠3. Corresponding angles would be same - position, e.g., ∠2 and ∠6. So ∠3 ≅ ∠6 by Alternate Interior Angles Theorem.

Answer:

alternate interior angles theorem