Question

question 14 of 40
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:

∠1 and ∠3 are positioned on opposite sides of the transversal, outside the two parallel lines A and B. This fits the definition of alternate exterior angles, which are congruent when formed by a transversal cutting parallel lines.

Answer:

A. Alternating exterior angles are congruent.