Question

∠stu≅∠rvs and ↔tu || ↔sv. complete the proof that ∠stu≅∠tuv.

statement reason
1 ∠stu≅∠rvs given
2 ↔tu || ↔sv given
3 ∠tuv≅∠rvs
4 ∠stu≅∠tuv alternate exterior angles theorem
alternate interior angles theorem
converse of alternate exterior angles theorem
converse of alternate interior angles theorem
converse of corresponding angles theorem

Explanation:

Step1: Recall parallel - line angle relationships

Since $\overleftrightarrow{TU}\parallel\overleftrightarrow{SV}$, and $\angle TUV$ and $\angle RVS$ are corresponding angles.

Step2: Apply the corresponding - angles theorem

When two parallel lines are cut by a transversal, corresponding angles are congruent. So, for $\overleftrightarrow{TU}\parallel\overleftrightarrow{SV}$ with transversal intersecting them, $\angle TUV\cong\angle RVS$ by the Corresponding Angles Theorem.

Answer:

Corresponding Angles Theorem