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) congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. This does not match the given condition of two angles and a non - included side.
• AAS (Angle - Angle - Side) congruence theorem 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) congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. The side here is included, so it does not match.
• HL (Hypotenuse - Leg) congruence theorem is used for right - triangles, where the hypotenuse and one leg of one right - triangle are congruent to the hypotenuse and one leg of another right - triangle. It does not apply to the given general triangle congruence situation with two angles and a non - included side.

Answer:

B. AAS