Which statement correctly identifies the SSS congruence criterion?

Which statement correctly identifies the SSS congruence criterion?

• A. Side-Side-Side
• B. Side-Angle-Side
• C. Angle-Side-Angle
• D. Angle-Angle-Side

Answer: (A)

Three equal corresponding sides fully determine triangle size and shape. When all three sides of one triangle match the three sides of another in the same order, the triangles can be laid over each other perfectly, so every corresponding angle and side coincides. That is the essence of the Side-Side-Side criterion: matching three sides guarantees congruence. The other names describe different ways to establish congruence: two sides with the included angle (SAS) use a side between known parts; two angles with a side (ASA or AAS) rely on angle information, with the side either between the known angles or adjacent to them. They are valid criteria too, but they refer to different information than three sides, which is why Side-Side-Side is the correct identification for this criterion.

Three equal corresponding sides fully determine triangle size and shape. When all three sides of one triangle match the three sides of another in the same order, the triangles can be laid over each other perfectly, so every corresponding angle and side coincides. That is the essence of the Side-Side-Side criterion: matching three sides guarantees congruence.

The other names describe different ways to establish congruence: two sides with the included angle (SAS) use a side between known parts; two angles with a side (ASA or AAS) rely on angle information, with the side either between the known angles or adjacent to them. They are valid criteria too, but they refer to different information than three sides, which is why Side-Side-Side is the correct identification for this criterion.