Which of the following must be true for two triangles to be congruent by the $SSS$ (Side-Side-Side) criterion?

• A. All three corresponding angles of the triangles are equal in measure.
• B. The sum of the sides of one triangle equals the sum of the sides of the other triangle.
• C. All three corresponding sides of the triangles are equal in length.
• D. Two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle.

Answer: (C)

Verified step by step guidance

1. Understand that the SSS (Side-Side-Side) criterion for triangle congruence states that if all three sides of one triangle are equal in length to the corresponding three sides of another triangle, then the two triangles are congruent.
2. Recall that congruence means the triangles are identical in shape and size, so all corresponding angles and sides match exactly.
3. Note that the SSS criterion does not require the angles to be given or compared directly; the equality of all three sides guarantees the angles will also be equal.
4. Recognize that the other options describe different criteria: equal angles alone do not guarantee congruence, the sum of sides being equal is not sufficient, and the two sides with included angle condition corresponds to the SAS (Side-Angle-Side) criterion, not SSS.
5. Therefore, the key condition for SSS congruence is that all three corresponding sides of the triangles are equal in length.