If three sides of two triangles are equal, what can be concluded?

• A. The triangles are congruent
• B. The triangles are similar
• C. The triangles have equal perimeters
• D. One is a reflection of the other

Answer: (A)

Having all three sides equal in length to the corresponding sides of another triangle means the two triangles have identical side lengths. This is enough to say they are congruent. When every pair of corresponding sides matches, the triangles are the same size and shape, and you can align one perfectly over the other using rigid motions (translations, rotations, or possibly reflections). This is the SSS condition for congruence: equal three sides determine congruence.

Similarity would require only proportional sides, which is weaker than having equal lengths. The fact that their perimeters are equal follows from congruence, but the essential conclusion is that the triangles are congruent. A reflection is not required to establish congruence—it’s just one of the possible rigid motions that could map one triangle onto the other.