Question

two angles and the non - included side of one triangle are congruent to the corresponding parts of another triangle. which congruence theorem can be used to prove that the triangles are congruent?
○ sss
○ aas
○ sas
○ hl

Explanation:

• SSS (Side - Side - Side): Requires three pairs of congruent sides. But the problem mentions two angles and a non - included side, so SSS is not relevant.
• AAS (Angle - Angle - Side): States that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, the triangles are congruent. This matches the given condition.
• SAS (Side - Angle - Side): Needs two sides and the included angle. The side here is non - included, so SAS is incorrect.
• HL (Hypotenuse - Leg): Applies only to right - angled triangles. There is no information about right angles in the problem, so HL is not applicable.

Answer:

B. AAS