Question

complete the proof that ∠prs ≅ ∠tuw.
statement reason
1 (overleftrightarrow{tv}paralleloverleftrightarrow{qs})
2 ∠tuw ≅ ∠qru
3 ∠qru ≅ ∠prs
4 ∠prs ≅ ∠tuw

Explanation:

Step1: Given parallel lines

Given in the problem setup.

Step2: Corresponding - angles postulate

If two parallel lines ($\overleftrightarrow{TV}$ and $\overleftrightarrow{QS}$) are cut by a transversal, then corresponding angles are congruent. So, $\angle TUW\cong\angle QRU$.

Step3: Vertical - angles theorem

Vertical angles are congruent. $\angle QRU$ and $\angle PRS$ are vertical angles, so $\angle QRU\cong\angle PRS$.

Step4: Transitive property of congruence

If $\angle TUW\cong\angle QRU$ and $\angle QRU\cong\angle PRS$, then by the transitive property of congruence, $\angle PRS\cong\angle TUW$.

Answer:

1. Given
2. Corresponding - angles postulate
3. Vertical - angles theorem
4. Transitive property of congruence