Question

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

2 horizontal lines are intersected by another line. At the intersection with the first line, the uppercase right angle is 91 degrees. At the intersection with the second line, the bottom right angle is 91 degrees.
2 horizontal lines are intersected by another line. At the intersection with the first line, uppercase right angle is 91 degrees and the bottom left angle is 91 degrees.
2 horizontal lines are intersected by another line. At the intersection with the first line, the uppercase right angle is 89 degrees and the bottom right angle is 91 degrees.
2 horizontal lines are intersected by another line. At the intersection with the first line, the bottom right angle is 91 degrees. At the intersection with the second line, the top right angle is 89 degrees.

Answer 1

Diagrams 1 and 4.

- Diagram 1: the upper‑right angle at the top line and the lower‑right angle at the bottom line are corresponding angles and are equal (91°), so the lines must be parallel.
- Diagram 4: the bottom‑right angle at the top line and the top‑right angle at the bottom line are consecutive interior angles and sum to 180° (91°+89°), so the lines must be parallel.

Diagrams 2 and 3 only give angle relations at a single intersection (vertical or adjacent angles), so they do not force the two lines to be parallel.