What does the AAS Congruence Criterion specify?

What does the AAS Congruence Criterion specify?

• A. Two angles and a non-included side
• B. Two sides and the included angle
• C. Side-angle-side
• D. Three sides

Answer: (A)

Two angles fix the shape of a triangle, since the third angle is determined by the fact that all three sum to 180 degrees. If you also know a side that is not between those two angles, that side fixes the overall size. With both the shape and the size known, the triangles must be congruent. This is the AAS congruence criterion: two angles and a non-included side suffice to prove two triangles are congruent. (Other common criteria include SAS, which uses two sides and the included angle, and SSS, which uses three sides.)

Two angles fix the shape of a triangle, since the third angle is determined by the fact that all three sum to 180 degrees. If you also know a side that is not between those two angles, that side fixes the overall size. With both the shape and the size known, the triangles must be congruent. This is the AAS congruence criterion: two angles and a non-included side suffice to prove two triangles are congruent. (Other common criteria include SAS, which uses two sides and the included angle, and SSS, which uses three sides.)