Question

Given: g ∥ h and ∠2 ≅ ∠3
Prove: e ∥ f

Horizontal and parallel lines e and f are intersected by diagonal and parallel lines g and h. At the intersection of lines g and e, the bottom right angle is angle 2. At the intersection of lines h and e, the bottom right angle is angle 1. At the intersection of lines f and h, the top left angle is angle 3.

Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorm
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?

vertical angles theorem
alternate exterior angles theorem
converse corresponding angles theorem
converse alternate interior angles theorem

Answer 1

converse alternate interior angles theorem

Reason: ∠1 and ∠3 are alternate interior angles formed by transversal h; since they are congruent, by the converse of the alternate interior angles theorem, e ∥ f.