Question

in exercises 16 - 18, use the diagram. 16. is r || s? 17. is m || n? 18. is s || t?

Explanation:

Step1: Recall parallel - line criteria

Parallel lines have equal corresponding angles, alternate - interior angles, etc. In the given diagram, we look for angle relationships.

Step2: Analyze \(r\) and \(s\)

There is no information (like equal angles) indicating that \(r\) and \(s\) are parallel. So \(r\) is not parallel to \(s\).

Step3: Analyze \(m\) and \(n\)

Since the corresponding angles formed by a transversal with \(m\) and \(n\) are right angles (marked by the square - shaped angle indicators), \(m\parallel n\) according to the corresponding - angles postulate (if corresponding angles are equal, the lines are parallel).

Step4: Analyze \(s\) and \(t\)

There are right - angle indicators between \(s\) and \(t\) and the transversals. By the corresponding - angles postulate, \(s\parallel t\).

Answer:

1. No
2. Yes
3. Yes