Question

complete the proof that tv || qs. statement 1. ∠prq ≅ ∠vwu 2. ∠prq ≅ ∠sru 3. ∠vwu ≅ ∠sru 4. tv || qs reason given vertical angle theorem transitive property of congruence angles forming a linear - pair sum to 180° converse of corresponding angles theorem corresponding angles theorem definition of supplementary angles vertical angle theorem

Explanation:

Step1: Identify given information

We are given that $\angle PRQ\cong\angle VUW$. This is the starting - point for our proof.

Step2: Use vertical - angle theorem

$\angle PRQ\cong\angle SRU$ because vertical angles are congruent. This is the vertical - angle theorem.

Step3: Apply transitive property

Since $\angle PRQ\cong\angle VUW$ and $\angle PRQ\cong\angle SRU$, by the transitive property of congruence, $\angle VUW\cong\angle SRU$.

Step4: Use converse of corresponding angles theorem

If $\angle VUW\cong\angle SRU$, then by the converse of the corresponding angles theorem, $\overleftrightarrow{TV}\parallel\overleftrightarrow{QS}$.

Answer:

1. Given
2. Vertical Angle Theorem
3. Transitive Property of Congruence
4. Converse of Corresponding Angles Theorem