Question

uw || rt. complete the proof that ∠rsv ≅ ∠svw.
statement reason
1 uw || rt given
2 ∠svw ≅ ∠qst
3 ∠qst ≅ ∠rsv
4 ∠rsv ≅ ∠svw transitive property of congruence

Explanation:

Step1: Identify given parallel lines

Given $\overleftrightarrow{UW}\parallel\overleftrightarrow{RT}$.

Step2: Use corresponding - angles property

$\angle SVW$ and $\angle QST$ are corresponding angles formed by the transversal intersecting $\overleftrightarrow{UW}$ and $\overleftrightarrow{RT}$, so $\angle SVW\cong\angle QST$ (Corresponding Angles Postulate).

Step3: Use vertical - angles property

$\angle QST$ and $\angle RSV$ are vertical angles. Vertical angles are congruent, so $\angle QST\cong\angle RSV$.

Step4: Apply transitive property

Since $\angle SVW\cong\angle QST$ and $\angle QST\cong\angle RSV$, by the Transitive Property of Congruence, $\angle RSV\cong\angle SVW$.

Answer:

The proof is completed as shown above with reasons being the Corresponding Angles Postulate, Vertical - Angles Theorem and Transitive Property of Congruence.