Practice Exam

Question 38 • Geometry: Concepts and Connections

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

Answer

Image with description Parallel lines are cut by a transversal. The first line intersecting the transversal creates 4 angles, the top right angle is labeled as 89 degrees, and the bottom right angle is labeled as 91 degrees.

Image with description Parallel lines are cut by a transversal. The first line intersecting the transversal creates 4 angles, the top right angle is labeled as 91 degrees, and the bottom left angle is labeled as 91 degrees.

Image with description Parallel lines are cut by a transversal. The first line intersecting the transversal creates 4 angles, the top right angle is labeled as 91 degrees. The second line intersecting the transversal creates 4 angles, the bottom right angle is labeled as 91 degrees.

Image with description Parallel lines are cut by a transversal. The first line intersecting the transversal creates 4 angles, the bottom right angle is labeled as 91 degrees. The second line intersects the transversal creating 4 angles, the top right angle is labeled as 89 degrees.

Explanation

In D, the 91° angle and the 89° angle are between the two lines and on the same side of the transversal. Their measures add to 91° + 89° = 180°. By the converse of the same-side interior angles theorem, the lines must be parallel.

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