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

The correct answer is:

The fourth diagram.

Explanation:

The fourth diagram has two same-side interior angles that are supplementary (add to 180°). The conerse of the same-side interior angle theorem states that if two lines are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel.

The diagram which shows lines that must be parallel lines cut by a transversal is:

This refers to two lines which can be found on the same plane, at an equidistance and does not meet.

With this in mind, we can see that from the given diagrams, there are parallel lines, but the only diagram which is cut by a transversal is the fourth diagram because it has supplementary angles which are 180°.

Read more about parallel lines here:

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