Question

ng a two - column proof
given: \\( \angle t \cong \angle v ; \overline{st} \parallel \overline{uv} \\)
prove: \\( \overline{tu} \parallel \overline{vw} \\)
complete the two - column proof.

Explanation:

Step1: Alternate Interior Angles Theorem

Since \( \overline{ST}\parallel\overline{UV}\), by the Alternate Interior Angles Theorem, \( \angle T\cong\angle U\).

Step2: Transitive Property of Congruence

Given \( \angle T\cong\angle V\) (Statement 3) and \( \angle T\cong\angle U\) (Statement 2), by the Transitive Property of Congruence, \( \angle U\cong\angle V\).

Step3: Converse Alternate Interior Angles Theorem

Since \( \angle U\cong\angle V\), by the Converse Alternate Interior Angles Theorem, \( \overline{TU}\parallel\overline{VW}\).

Answer:

1. alternate interior angles theorem; 4. transitive property of congruence; 5. converse alternate interior angles theorem