Similarity, Right Triangle Trigonometry, and Proof: Part One — Test

Question 14 • 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 slanted transversal. At the upper intersection, the angle above the upper line and to the left of the transversal is labeled 65 degrees, and the angle below the upper line and to the right of the transversal is labeled 65 degrees. No angle measure is shown at the lower intersection.

Image with description Two left-to-right lines are crossed by a slanted transversal. At the upper intersection, the angle below the upper line and to the left of the transversal is labeled 115 degrees, and the angle below the upper line and to the right of the transversal is labeled 65 degrees. No angle measure is shown at the lower intersection.

Image with description Two left-to-right lines are crossed by a slanted transversal. At the upper intersection, the angle above the upper line and to the right of the transversal is labeled 115 degrees. At the lower intersection, the angle above the lower line and to the left of the transversal is labeled 115 degrees.

Image with description Two left-to-right lines are crossed by a slanted transversal. At the upper intersection, the angle below the upper line and to the left of the transversal is labeled 115 degrees. At the lower intersection, the angle above the lower line and to the left of the transversal is labeled 65 degrees.

Explanation

In A, the two labeled angles lie between the lines and on the same side of the transversal. They add to 115° + 65° = 180°. By the converse of the same-side interior angles theorem, if these angles are supplementary, the lines must be parallel.

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