ASA Congruence Criterion requires which arrangement of parts?

ASA Congruence Criterion requires which arrangement of parts?

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

Answer: (D)

Two angles with the side between them determine a triangle uniquely. This is the ASA (Angle-Side-Angle) idea: if you know two angles and the included side, the shape is fixed by the angles and the exact size is fixed by that side, so the corresponding parts of both triangles must match exactly. The side must be the one between the two angles, called the included side, which is why the arrangement is two angles with the side in between. If you only had two angles (AAA), you’d get similarity, not necessarily congruence, because sizes could differ. Other congruence patterns use different pieces (two sides and the included angle, or all three sides) and don’t match this specific ASA setup.

Two angles with the side between them determine a triangle uniquely. This is the ASA (Angle-Side-Angle) idea: if you know two angles and the included side, the shape is fixed by the angles and the exact size is fixed by that side, so the corresponding parts of both triangles must match exactly. The side must be the one between the two angles, called the included side, which is why the arrangement is two angles with the side in between. If you only had two angles (AAA), you’d get similarity, not necessarily congruence, because sizes could differ. Other congruence patterns use different pieces (two sides and the included angle, or all three sides) and don’t match this specific ASA setup.