To determine if two triangles are congruent, we need to know which sides and angles are included.
The SSA (Side-Side-Angle) criterion does not guarantee triangle congruence as it could lead to ambiguous cases (the "Ambiguous Case" in triangle construction).
ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) both guarantee triangle congruence, as they use two angles and a corresponding side.
SAS (Side-Angle-Side) also guarantees congruence by having two sides and the included angle.
HL (Hypotenuse-Leg) applies specifically to right triangles.
SSS (Side-Side-Side) guarantees congruence when all three sides are known.
Without additional context about the specifics of the triangles in question, the most common congruence criteria typically applied are ASA, AAS, SAS, or SSS.
If you provide more specific information about the triangles in question, I can help identify which theorem applies directly to prove their congruence. However, if there's no specific information beyond "they can be proved congruent," you might opt for either ASA, AAS, SAS, or SSS based on common scenarios.
If I'm to select the most general applicable theorem from your options, it would be SSS or SAS, assuming all sides or necessary angle-side combinations are given. If you have any specifics to share regarding angles or sides, that would assist in selecting the correct theorem conclusively.
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