Triangle Congruence — Test

Question 14 • Geometry

Which pair of triangles can be proven congruent by SAS?

Answer

Image with description Two triangles share one side. The shared side has a tick mark. A pair of angles at one endpoint of the shared side have matching single arc marks, and a pair of angles at the other endpoint have matching double arc marks.

Image with description A triangle is divided into two right triangles by a segment from the top vertex to the base. The shared segment has double tick marks, the two base segments have matching single tick marks, and right-angle markers are shown where the shared segment meets the base.

Image with description Two triangles share a diagonal side. The shared diagonal has triple tick marks. One pair of outer sides has matching single tick marks, and another pair of outer sides has matching double tick marks.

Image with description Two separate triangles are shown. In the left triangle, the bottom side has a single tick mark, the right slanted side has double tick marks, and the angle at the left endpoint of the bottom side has an arc mark. In the right triangle, the left vertical side has a single tick mark, the upper slanted side has double tick marks, and the angle at the lower endpoint of the vertical side has an arc mark.

Explanation

SAS requires two pairs of corresponding sides and the angle between those sides to match. In choice D, the shared segment is equal to itself, the two base segments have matching tick marks, and the marked right angles lie between those sides in each triangle. Therefore, the triangles are congruent by SAS.

AI-written and checked against the verified answer.

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