Practice Exam

Question 19 • MASTER COURSE Geometry

Which pair of triangles can be proven congruent by SAS?

Answer

Image with description Two separate, unlabeled triangles are shown with the same orientation. In each triangle, the top angle has double arc marks, the lower-left angle has triple arc marks, and the lower-right angle has one arc mark. No side tick marks are shown.

Image with description Two unlabeled triangles meet at a central intersection point. A nearly horizontal segment passes through the intersection; the segment on each side of the intersection has matching single tick marks. A slanted segment also passes through the intersection; the segment on each side of the intersection has matching double tick marks. Matching angle marks are shown at the intersection between the single-tick and double-tick sides of each triangle.

Image with description A figure is divided into two unlabeled triangles by a segment from the top vertex to a lower center vertex. The dividing segment has double tick marks. A single arc mark spans the full angle at the top vertex between the two outer sides. Matching double arc marks are shown at the lower-left vertex and the right vertex.

Image with description A large unlabeled triangle is divided into two smaller triangles by a vertical segment from the top vertex to the base. The two outer slanted sides have matching single tick marks, the shared vertical segment has a single tick mark, and right-angle markers are shown where the vertical segment meets the base.

Explanation

In choice C, each triangle has two corresponding sides marked equal: the single-tick sides match, and the double-tick sides match. The marked angles at the intersection are the angles included between those two sides, and they are equal. Two sides and their included angle establish congruence by SAS.

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