Question

uw || rt. complete the proof that ∠rsv ≅ ∠svw.
statement\treason
1 uw || rt\tgiven
2 ∠svw ≅ ∠qst
3 ∠qst ≅ ∠rsv
4 ∠rsv ≅ ∠svw

Explanation:

Step1: Identify vertical - angle property

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

Step2: Identify vertical - angle property again

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

Step3: Use transitive property of congruence

If $\angle SVW\cong\angle QST$ and $\angle QST\cong\angle RSV$, then by the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$ for congruent angles), $\angle RSV\cong\angle SVW$.

Answer:

1. Reason: Vertical angles are congruent.
2. Reason: Vertical angles are congruent.
3. Reason: Transitive property of congruence.