Question

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

Explanation:

Step1: Identify angle - pair relationship

When two parallel lines ($\overleftrightarrow{QS}\parallel\overleftrightarrow{TV}$) are cut by a transversal, $\angle TUW$ and $\angle QRU$ are corresponding angles. So, by the Corresponding Angles Postulate, $\angle TUW\cong\angle QRU$.

Step2: Identify vertical - angle relationship

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

Step3: Use the transitive property

Since $\angle TUW\cong\angle QRU$ and $\angle QRU\cong\angle PRS$, by the Transitive Property of Congruence, $\angle PRS\cong\angle TUW$.

Answer:

1. Corresponding Angles Postulate; 3. Vertical Angles Theorem; 4. Transitive Property of Congruence