Question

1. choose the correct answer.

which theorem or postulate shows that ∠3 ≅ ∠6?
alternate exterior angles theorem
vertical angles theorem
alternate interior angles theorem
corresponding angles postulate

Explanation:

• Alternate Exterior Angles Theorem: Applies to angles outside the two parallel lines, which is not the case for \(∠3\) and \(∠6\).
• Vertical Angles Theorem: Applies to pairs of opposite angles formed by intersecting lines, not relevant here.
• Alternate Interior Angles Theorem: States that when a transversal intersects two parallel lines, alternate interior angles are congruent. \(∠3\) and \(∠6\) are alternate interior angles (between the parallel lines \(l\) and \(m\) and on opposite sides of the transversal \(t\)).
• Corresponding Angles Postulate: Applies to angles in the same relative position, not \(∠3\) and \(∠6\).

Answer:

Alternate Interior Angles Theorem