Given: a ∥ b and ∠1 ≅ ∠3

Prove: e ∥ f


Horizontal and parallel lines e and f are intersected by parallel lines a and b. At the intersection of lines a and e, the bottom left angle is angle 1. At the intersection of lines b and e, the uppercase right angle is angle 2. At the intersection of lines f and b, the bottom left angle is angle 3 and the bottom right angle is angle 4.


We know that angle 1 is congruent to angle 3 and that line a is parallel to line b because they are given. We see that __________ by the alternate exterior angles theorem. Therefore, angle 2 is congruent to angle 3 by the transitive property. So, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem.


Which information is missing in the paragraph proof?


∠2 ≅ ∠4

∠1 ≅ ∠2

∠2 ≅ ∠3

∠1 ≅ ∠4