Which congruence criterion applies when two sides and the included angle are congruent?

Which congruence criterion applies when two sides and the included angle are congruent?

• A. SSS
• B. SAS
• C. ASA
• D. AAS

Answer: (B)

Two triangles are fixed uniquely when you know two sides and the angle between them. That included angle sits between those two sides, so knowing those three pieces determines the shape and size of the triangle exactly, guaranteeing congruence. This is the side-angle-side (SAS) criterion: if two sides and the included angle of one triangle equal the corresponding parts of another triangle, the triangles are congruent. Other criteria rely on different information: three sides (SSS) fixes the triangle by all three lengths, while two angles with a side (ASA or AAS) use angle information in different positions. But with two sides and the included angle, SAS is the exact match.

Two triangles are fixed uniquely when you know two sides and the angle between them. That included angle sits between those two sides, so knowing those three pieces determines the shape and size of the triangle exactly, guaranteeing congruence. This is the side-angle-side (SAS) criterion: if two sides and the included angle of one triangle equal the corresponding parts of another triangle, the triangles are congruent.

Other criteria rely on different information: three sides (SSS) fixes the triangle by all three lengths, while two angles with a side (ASA or AAS) use angle information in different positions. But with two sides and the included angle, SAS is the exact match.