Which statement correctly identifies the SAS congruence criterion?

Which statement correctly identifies the SAS congruence criterion?

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

Answer: (B)

Two sides and the angle between those sides uniquely determine a triangle, which is the essence of a congruence criterion. If two triangles have two sides congruent to each other and the included angle between those sides congruent as well, the triangles must be congruent. The key is that the angle sits between the two known sides — that’s what makes this a reliable criterion. If the angle you know isn’t the angle between the two given sides, that information isn’t enough to guarantee congruence, because you can end up with different shapes that share the same data. So the statement identifies the Side-Angle-Side criterion.

Two sides and the angle between those sides uniquely determine a triangle, which is the essence of a congruence criterion. If two triangles have two sides congruent to each other and the included angle between those sides congruent as well, the triangles must be congruent. The key is that the angle sits between the two known sides — that’s what makes this a reliable criterion. If the angle you know isn’t the angle between the two given sides, that information isn’t enough to guarantee congruence, because you can end up with different shapes that share the same data. So the statement identifies the Side-Angle-Side criterion.