Question

four lines and four congruent angles are identified in the diagram. which statement must be true? a only a||b b no pair of lines are parallel. c only r||s d a||b and r||s

Explanation:

Step1: Recall parallel - line angle rules

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Step2: Analyze angles for \(a\) and \(b\)

The angles formed by the transversals \(r\) and \(s\) with lines \(a\) and \(b\) are congruent. For example, the angles at the intersection of \(r\) with \(a\) and \(r\) with \(b\) are both \(93.7^{\circ}\). So, \(a\parallel b\) by the corresponding - angles postulate.

Step3: Analyze angles for \(r\) and \(s\)

The angles formed by the transversals \(a\) and \(b\) with lines \(r\) and \(s\) are congruent. For example, the angles at the intersection of \(a\) with \(r\) and \(a\) with \(s\) are both \(93.7^{\circ}\). So, \(r\parallel s\) by the corresponding - angles postulate.

Answer:

D. \(a\parallel b\) and \(r\parallel s\)