Practice Test

Question 12 • Mathematics II

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

Answer

Image with description Two left-to-right lines are crossed by a vertical transversal. At the upper intersection, the angle below the line and to the right of the transversal is labeled 91 degrees. At the lower intersection, the angle above the line and to the right of the transversal is labeled 89 degrees.

Image with description Two left-to-right lines are crossed by a vertical transversal. At the upper intersection, the angle above the line and to the right of the transversal is labeled 91 degrees, and the angle below the line and to the left of the transversal is labeled 91 degrees. No angle measure is shown at the lower intersection.

Image with description Two left-to-right lines are crossed by a vertical transversal. At the upper intersection, the angle above the line and to the right of the transversal is labeled 89 degrees, and the angle below the line and to the right of the transversal is labeled 91 degrees. No angle measure is shown at the lower intersection.

Image with description Two left-to-right lines are crossed by a vertical transversal. At the upper intersection, the angle above the line and to the right of the transversal is labeled 91 degrees. At the lower intersection, the angle below the line and to the right of the transversal is labeled 91 degrees.

Explanation

In B, the two marked angles are interior angles on the same side of the transversal. For the lines to be parallel, same-side interior angles must be supplementary. Since 91° + 89° = 180°, the lines must be parallel. The angle pairs in C and D are at a single intersection, so they do not establish that the two lines are parallel.

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