Triangle Congruence — Test

Question 14 • Geometry

Which pair of triangles can be proven congruent by SAS?

Answer

Image with description 2 congruent triangles have a common altitude, congruent angles at the vertex, and congruent base angles at the altitude.

Image with description 2 triangles have congruent bases, congruent side lengths, and congruent angles that are not included between two congruent sides.

Image with description 2 triangles have a common side, 2 congruent bases, and 2 congruent altitudes.

Image with description A triangle has no labels. A perpendicular bisector is drawn from the vertex to the opposite base and divides the base into 2 equal halves, so 2 identical triangles are formed.

Explanation

The perpendicular bisector divides the base into two equal segments, and the altitude is a shared side of the two smaller triangles. The angle between each base segment and the altitude is 90°, so those included angles are congruent. Thus the triangles have two pairs of congruent sides and the included angle congruent, which proves SAS.

AI-written and checked against the verified answer.

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