Question

complete the proof that ∠prs≅∠tuw.
statement

1. tv || qs
2. ∠tuw≅∠qru
3. ∠qru≅∠prs
4. ∠prs≅∠tuw

reason
given
corresponding angles theorem

Explanation:

Step1: Identify given information

Given $TV\parallel QS$.

Step2: Use corresponding - angles theorem

Since $TV\parallel QS$, $\angle TUW\cong\angle QRU$ (corresponding - angles theorem).

Step3: Another pair of corresponding angles

Also, $\angle QRU\cong\angle PRS$ (corresponding - angles for another set of parallel - like relationships in the figure).

Step4: Apply 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:

The proof is completed by using the corresponding - angles theorem and the transitive property of congruence to show that $\angle PRS\cong\angle TUW$.