Proving Lines Parallel — Quiz

Question 5 • Geometry: Concepts and Connections

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

Answer

Image with description Parallel lines s and r are cut by transversal m. Line s intersecting transversal m creates 4 angles, the top left angle is labeled as 89 degrees, and the top right angle is labeled as 91 degrees.

Image with description Parallel lines s and r are cut by transversal m. Line s intersecting transversal m creates 4 angles, the top right angle is labeled as 91 degrees. Line r intersecting transversal m creates 4 angles, the top right angle is labeled as 91 degrees.

Image with description Parallel lines s and r are cut by transversal m. Line s intersecting transversal m creating 4 angles, the top left angle is labeled as 89 degrees, and the bottom right angle is labeled as 89 degrees.

Image with description Parallel lines s and r are cut by transversal m. Line s intersecting transversal m creates 4 angles, the top left angle is labeled as 89 degrees. Line r intersecting transversal m creates 4 angles, the bottom right angle is labeled as 91 degrees.

Explanation

In choice A, the two top-right angles are corresponding angles: they occupy the same position at the two intersections. Both measure 91°, so they are congruent. By the converse of the corresponding angles theorem, the two lines must be parallel. The equal or supplementary angles in choices B and C occur at just one intersection and do not establish that the lines are parallel.

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