Step | Description | Justification |
1 | Let a || b | This is a criterion, a necessary condition. |
2 | To show: ∠5 ≅ ∠3 and ∠4 ≅ ∠6. | The goal is to show that alternate exterior angles are congruent. |
3 | ∠5 ≅ ∠1 | The Parallel Line Postulate states that, given a transversal of parallel lines, corresponding angles are congruent. |
4 | ∠1 ≅ ∠3 | The Vertical Angle Theorem states that vertical angles are congruent. |
5 | ∠5 ≅ ∠3 | The Transitivity of Congruence of Angles Theorem states that if two angles are congruent to the same angle, they are congruent to each other. In this case since ∠5 ≅ ∠1 and ∠1 ≅ ∠3, so ∠5 ≅ ∠3. A similar argument can be made to show that ∠4 ≅ ∠6. Q.E.D. |
Table 1: Proof of the Alternate Exterior Angles Theorem |