Triangle Congruence — Test

Question 14 • Mathematics I

Which pair of triangles can be proven congruent by SAS?

Answer

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.

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.

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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