Question

1. which of the following diagrams represent the consecutive interior angles theorem and its converse

Explanation:

Step1: Analyze the first option

The first option shows the transitive property of parallel lines, not the Consecutive Interior Angles Theorem and its converse.

Step2: Analyze the second option

The second option shows angles \(1\) and \(8\), which are not consecutive interior angles.

Step3: Analyze the third option

The third option shows angles \(2\) and \(6\), which are alternate interior angles (by the Alternate Interior Angles Theorem, if \(j\parallel k\), then \(\angle2\cong\angle6\)), not consecutive interior angles.

Step4: Analyze the fourth option

The fourth option shows angles \(3\) and \(5\). By the Consecutive Interior Angles Theorem, if \(j\parallel k\), then \(\angle3+\angle5 = 180^{\circ}\) (they are supplementary). By the Consecutive Interior Angles Converse, if \(\angle3\) and \(\angle5\) are supplementary, then \(j\parallel k\).

Answer:

The fourth option (the one with angles \(3\) and \(5\) where if \(\angle3\) and \(\angle5\) are supplementary, then \(j\parallel k\))