Question

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

Explanation:

Answer:

The diagram with the two horizontal lines (parallel candidates) cut by a vertical transversal, where the corresponding angles (or alternate interior angles, or consecutive interior angles that satisfy the parallel line condition) are both \(91^\circ\) (for example, if they are alternate interior angles or corresponding angles, equal angles imply parallel lines; if it's the first diagram with the two \(91^\circ\) angles in corresponding positions, that shows parallel lines cut by a transversal. The second diagram with a \(91^\circ\) and its adjacent angle (which would be supplementary if parallel, but \(91 + 91
eq 180\), so the first diagram is the one where the angle relationship enforces parallelism). So the answer is the first diagram (the one with two horizontal lines, vertical transversal, both \(91^\circ\) angles in the same relative position, like corresponding angles or alternate interior angles equal, proving parallelism).

(Note: Since the exact diagram labels aren't given, but based on angle relationships: when two lines are cut by a transversal, if corresponding angles are equal, alternate interior angles are equal, or consecutive interior angles are supplementary, the lines are parallel. The first diagram likely has equal corresponding/alternate interior angles (both \(91^\circ\)), so that's the one with parallel lines. The second has a \(91^\circ\) and another \(91^\circ\) adjacent, which would not be supplementary, so not enforcing parallelism. So the answer is the first option (the top diagram with two horizontal lines, vertical transversal, both \(91^\circ\) angles in the "same side" relative to the transversal, like corresponding angles).)