Question

which is enough information to prove that s || t? ∠1 ≅ ∠3 ∠5 + ∠6 = 180° ∠1 + ∠4 = 180° ∠2 ≅ ∠8

Explanation:

Step1: Analyze each option

• For $\angle1\cong\angle3$: Vertical angles are always congruent, this has nothing to do with proving \(s\parallel t\).
• For $\angle5+\angle6 = 180^{\circ}$: These are adjacent angles on a straight line (linear - pair), their sum being \(180^{\circ}\) is a property of adjacent angles on a line, not related to parallel lines.
• For $\angle1+\angle4=180^{\circ}$: These are adjacent angles on a straight line (linear - pair), their sum being \(180^{\circ}\) is a property of adjacent angles on a line, not related to parallel lines.
• For $\angle2\cong\angle8$: If two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. Here, \(\angle2\) and \(\angle8\) are corresponding angles. If \(\angle2\cong\angle8\), then by the converse of the corresponding angles postulate, \(s\parallel t\).

Answer:

\(\angle2\cong\angle8\)