Question

if ∠1 ≅ ∠2, which of the following can be concluded?
s is ⊥ u by converse of alternate interior angles thm
v ⊥ r by converse of alternate exterior angles thm
u is parallel to v by converse of corresponding angles thm
r is parallel to s by converse of corresponding angles thm

Explanation:

To solve this, we use the Converse of the Corresponding Angles Theorem. The theorem states that if two corresponding angles are congruent, then the two lines cut by a transversal are parallel. Here, ∠1 and ∠2 are corresponding angles. If ∠1 ≅ ∠2, then lines r and s (or the relevant lines; from the options, the correct one is about r being parallel to s by the Converse of Corresponding Angles Thm). Wait, looking at the options: the teal option says "r is parallel to s by Converse of Corresponding Angles Thm." Let's analyze: ∠1 and ∠2 are corresponding angles formed by transversal (let's say) and lines r and s. So by Converse of Corresponding Angles Theorem, if corresponding angles are congruent, lines are parallel. So the correct option is the teal one: "r is parallel to s by Converse of Corresponding Angles Thm."

Answer:

r is parallel to s by Converse of Corresponding Angles Thm. (The teal - colored option: "r is parallel to s by Converse of Corresponding Angles Thm.")