Question

a student was given the following diagram and asked to prove that $angle 1 cong angle 2$. what would be the reason for the second step in the proof?
given: line a and line b are parallel.
prove: $angle 1 cong angle 2$

statements

1. line a and line b are parallel
2. $angle 1 cong angle 3$
3. $angle 2 cong angle 3$
4. $angle 1 cong angle 2$

reasons

1. given

a. alternating exterior angles are congruent.
b. definition of supplementary angles
c. alternating interior angles are congruent.
d. corresponding angles are congruent.

Explanation:

First, identify the relationship between ∠1 and ∠3. ∠1 and ∠3 are on opposite sides of the transversal, outside the parallel lines A and B. This fits the definition of alternate exterior angles, which are congruent when formed by a transversal cutting parallel lines. This is the logical second step to link to proving ∠1 ≅ ∠2 (since ∠3 and ∠2 are vertical angles, congruent in step 3, then transitive property in step 4).

Answer:

A. Alternating exterior angles are congruent.