Question

statement

1. ( l parallel n )
2. ( angle 3 cong angle 2 )
3. ( angle 2 cong angle 1 )
4. ( angle 3 cong angle 1 )

reason

1. given
2. ?
3. vertical angles theorem
4. transitive property of congruence

which theorem justifies step 2?
corresponding angles theorem
vertical angles theorem
alternate interior angles theorem
alternate exterior angles theorem

Explanation:

• Corresponding Angles Theorem: States that if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. But this does not apply here as the angles in question are not in corresponding positions.
• Vertical Angles Theorem: Already used in Step 3. Vertical angles are formed by two intersecting lines. Here, the relationship in Step 2 is due to parallel lines and a transversal, not just two intersecting lines.
• Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. But ∠3 and ∠2 are not alternate interior angles.
• Alternate Exterior Angles Theorem: If two parallel lines \(l\parallel n\) are cut by a transversal, then alternate exterior angles (in this case, ∠3 and ∠2) are congruent.

Answer:

Alternate Exterior Angles Theorem