Question

tv || qs. complete the proof that ∠prs ≅ ∠tuw. statement reason 1 tv || qs given 2 ∠tuw ≅ ∠qru 3 ∠qru ≅ ∠prs 4 ∠prs ≅ ∠tuw

Explanation:

Step1: Identify corresponding - angles

Since $\overleftrightarrow{TV}\parallel\overleftrightarrow{QS}$, $\angle TUW$ and $\angle QRU$ are corresponding angles. By the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then the corresponding angles are congruent. So, $\angle TUW\cong\angle QRU$.

Step2: Identify vertical - angles

$\angle QRU$ and $\angle PRS$ are vertical angles. By the Vertical Angles Theorem, vertical angles are congruent. So, $\angle QRU\cong\angle PRS$.

Step3: Use the transitive property

The transitive property of congruence states that if $\angle A\cong\angle B$ and $\angle B\cong\angle C$, then $\angle A\cong\angle C$. Since $\angle TUW\cong\angle QRU$ and $\angle QRU\cong\angle PRS$, we can conclude that $\angle PRS\cong\angle TUW$.

Answer:

1. Corresponding Angles Postulate
2. Vertical Angles Theorem
3. Transitive Property of Congruence