Question

quadrilateral sr ty is shown.
given: ∠syt ≅ ∠trs, rs || yt
prove: △tys ≅ △srt
an incomplete two - column proof is shown.

1. ∠syt ≅ ∠trs, rs || yt: given
2. st ≅ st: reflexive property of congruence
3. ∠yts ≅ ∠rst:
4. △tys ≅ △srt: 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 \(RS\parallel YT\) and we need to find the reason for \(\angle YTS\cong\angle RST\).

Step2: Recall the properties of parallel lines

When two parallel lines (\(RS\) and \(YT\)) are intersected by a transversal (\(ST\)), alternate interior angles are congruent.

Answer:

If two parallel lines are intersected by a transversal, then alternate interior angles are congruent.