Final answer:
The correct theorems to prove that two triangles are congruent are SAS (Side-Angle-Side) and ASA (Angle-Side-Angle). AAA cannot be used for congruence proof as it lacks side length information, and SSA is not a valid condition for proving congruence. Therefore, the correct options are B and C.
Step-by-step explanation:
The question is about determining which theorem can be used to prove that two triangles are congruent. In the context of triangles and their properties, there are several theorems that can be used to prove congruence. However, not all sets of given conditions will necessarily prove that two triangles are congruent. Among the options provided:
• AAA (Angle-Angle-Angle) specifies that all three angles in one triangle are congruent to all three angles in another triangle. This does not prove congruence because it does not include any side length information.
• SAS (Side-Angle-Side) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, the triangles are congruent.
• ASA (Angle-Side-Angle) asserts that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.
• SSA (Side-Side-Angle) involves two sides and a non-included angle. This is not a valid condition for proving triangle congruence.
Therefore, the correct options that can be used to prove that two triangles are congruent are B) SAS (Side-Angle-Side) and C) ASA (Angle-Side-Angle). It is important to mention the correct option in the final answer. SSA and AAA do not prove triangle congruence and can lead to ambiguous cases.