Question: Complete the proof that $\angle V \cong \angle TWX$.\nW\nT\nU\nV\nX\nStatement\tReason\n1\tsegmentlineTW is parallel to segmentlineUVline\nTW\n\parallel\line\nUV\nGiven\n2\t$\angle WTX$ is congruent to $\angle U$\n$\angle WTX \cong \angle U$\nGiven\n3\t$\angle WTX$ is congruent to $\angle V$\n$\angle WTX \cong \angle V$\nText field with dropdown. Use the down arrow key to hear the options, press spacebar to select. Alternate Exterior Angles Theorem Alternate Interior Angles Theorem Converse of Alternate Exterior Angles Theorem Converse of Alternate Interior Angles Theorem Converse of Corresponding Angles Theorem Converse of Same-Side Exterior Angles Theorem Converse of Same-Side Interior Angles Theorem Corresponding Angles Theorem Reflexive Property of Congruence Reflexive Property of Equality Same-Side Exterior Angles Theorem Same-Side Interior Angles Theorem Substitution Transitive Property of Congruence Transitive Property of Equality\n4\t$\angle U$ is congruent to $\angle TWX$\n$\angle U \cong \angle TWX$\nAlternate Interior Angles Theorem\n5\t$\angle WTX$ is congruent to $\angle TWX$\n$\angle WTX \cong \angle TWX$\nText field with dropdown. Use the down arrow key to hear the options, press spacebar to select. Alternate Exterior Angles Theorem Alternate Interior Angles Theorem Converse of Alternate Exterior Angles Theorem Converse of Alternate Interior Angles Theorem Converse of Corresponding Angles Theorem Converse of Same-Side Exterior Angles Theorem Converse of Same-Side Interior Angles Theorem Corresponding Angles Theorem Reflexive Property of Congruence Reflexive Property of Equality Same-Side Exterior Angles Theorem Same-Side Interior Angles Theorem Substitution Transitive Property of Congruence Transitive Property of Equality\n6\t$\angle V$ is congruent to $\angle TWX$\n$\angle V \cong \angle TWX$\nTransitive Property of Congruence
1. **State the problem:** Complete the proof that $\angle V \cong \angle TWX$.\n\n2. **Given:** $\overline{TW} \parallel \overline{UV}$ and $\angle WTX \cong \angle U$.\n\n3. **Step 1:** Since $\overline{TW} \parallel \overline{UV}$ and $TX$ is a transversal, by the \textbf{Alternate Interior Angles Theorem}, we have:\n$$\angle WTX \cong \angle V.$$\n\n4. **Step 2:** Given $\angle WTX \cong \angle U$, and from Step 1 $\angle WTX \cong \angle V$, by the \textbf{Transitive Property of Congruence}, we get:\n$$\angle U \cong \angle V.$$\n\n5. **Step 3:** Since $\overline{TW} \parallel \overline{UV}$ and $WX$ is a transversal, by the \textbf{Alternate Interior Angles Theorem}, we have:\n$$\angle U \cong \angle TWX.$$\n\n6. **Step 4:** From Step 2 and Step 3, by the \textbf{Transitive Property of Congruence}, we conclude:\n$$\angle V \cong \angle TWX.$$\n\nThis completes the proof that $\angle V \cong \angle TWX$.