What condition guarantees triangle congruence by the SSS criterion?

• A. All three angles are equal
• B. The corresponding sides of two triangles are equal in length
• C. A pair of angles and the included side are equal
• D. The sum of corresponding sides is equal

Answer: (B)

Congruence via the SSS rule is guaranteed when every corresponding side of one triangle has the same length as the corresponding side of the other triangle. If you know all three side lengths match exactly, the shape is fixed up to rigid motions (you can move one triangle to line up with the other using rotations, translations, or reflections), so the two triangles are congruent.

This is stronger than just equal angles, which can give similar triangles of different sizes. It’s also a different criterion from other congruence rules like two sides with the included angle, or one angle with two sides. Simply having the sums of sides equal doesn’t ensure the same triangle shape or size.