Answer:
1. given
2. corresponding angle theorem
3. vertical angle theorem
4. transitive
Explanation:
1. it is given because the question supplies the fact at the top above the diagram called "Given:"
2. corresponding angle theorem: "when a line intersects 2 parallel lines, then the corresponding angles in the 2 regions of intersection are congruent" (also look at correspond_screenshot, the first image)
3. vertical angle theorem: "when two straight lines intersect, they form two sets of linear pairs with congruent angles" (also look at vertical_screenshot, the second image)
4. transitive: since we now know <2 ~= <1 ~= <3, we can say <2 ~= <3
("If any segments or angles are congruent to the same angle, then they are congruent to each other")