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: Recall vertical - angle property

$\angle SVW$ and $\angle QST$ are vertical angles, so $\angle SVW\cong\angle QST$ (Vertical angles are congruent).

Step3: Recall vertical - angle property again

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

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 using the given parallel - line information and the properties of vertical angles and the transitive property of congruence.