Question

which diagram shows lines that must be parallel lines cut by a transversal?

Explanation:

Step1: Recall the property of parallel lines cut by a transversal

When two parallel lines are cut by a transversal, alternate interior angles are equal.

Step2: Analyze each diagram

• In the first diagram: The two angles of \(89^{\circ}\) are alternate interior angles. If alternate interior angles are equal, then the lines \(s\) and \(r\) are parallel.
• In the second diagram: One angle is \(89^{\circ}\) and the other is \(91^{\circ}\), they are not equal, so no conclusion of parallelism.
• In the third diagram: The two \(91^{\circ}\) angles are not in the position of alternate interior angles for lines \(s\) and \(r\).
• In the fourth diagram: \(89^{\circ}\) and \(91^{\circ}\) are not equal and not in the correct position for parallel - line determination.

Answer:

The first diagram.