Question

given: ∠syt ≅ ∠trs, (overline{rs}paralleloverline{yt}) prove: (\triangle tyscong\triangle srt) an incomplete two - column proof is shown. 1. ∠syt ≅ ∠trs, (overline{rs}paralleloverline{yt}) 1. given 2. (overline{st}congoverline{st}) 2. reflexive property of congruence 3. ∠yts ≅ ∠rst 3. 4. (\triangle tyscong\triangle srt) 4. aas congruence what reason can be used to justify the statement in step 3? if two parallel lines are intersected by a transversal then alternate exterior angles are congruent if two parallel lines are intersected by a transversal then corresponding angles are congruent if two parallel lines are intersected by a transversal then alternate interior angles are congruent vertical angles theorem

Explanation:

Step1: Analyze the given information

We have \(RS\parallel YT\). When two parallel lines (\(RS\) and \(YT\)) are cut by a transversal (\(ST\)), the alternate - interior angles are congruent.

Step2: Identify the angles

The transversal \(ST\) cuts the parallel lines \(RS\) and \(YT\). The angles \(\angle YTS\) and \(\angle RST\) are alternate - interior angles.

Answer:

Alternate - interior angles theorem.