Angle Congruence 070246

1. **State the problem:** We are given that line $FH \parallel QS$ and line $TV \parallel FH$. We need to prove that $\angle PRS \cong \angle TUW$. 2. **Given statements:** - $FH \parallel QS$ (Given) - $TV \parallel FH$ (Given) 3. **Step 3:** $\angle TUW \cong \angle FGW$ by the **Alternate Exterior Angles Theorem** because $TV \parallel FH$ and $UW$ is a transversal. 4. **Step 4:** $\angle FGW \cong \angle PRS$ by the **Alternate Exterior Angles Theorem** because $FH \parallel QS$ and $GW$ is a transversal. 5. **Step 5:** By the **Transitive Property of Congruence**, since $\angle TUW \cong \angle FGW$ and $\angle FGW \cong \angle PRS$, it follows that $\angle PRS \cong \angle TUW$. **Final conclusion:** $\boxed{\angle PRS \cong \angle TUW}$