To determine which theorem allows us to prove two triangles congruent, we need to know specific details about the triangles, such as the lengths of their sides or the measures of their angles.
However, generally speaking:
- HL (Hypotenuse-Leg): This applies only to right triangles where one leg and the hypotenuse of one triangle is equal to the corresponding leg and hypotenuse of another triangle.
- AAS (Angle-Angle-Side): This method can be used when two angles and a non-included side of one triangle are known to be congruent to two angles and the corresponding non-included side of another triangle.
- ASA (Angle-Side-Angle): This method is used when two angles and the included side are known to be congruent in both triangles.
- SSS (Side-Side-Side): This method is used when the three sides of one triangle are equal to the three sides of another triangle.
- SAS (Side-Angle-Side): This method is used when two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
- SSA (Side-Side-Angle): This condition does not generally prove triangles congruent due to the possibility of forming two different triangles (ambiguous case).
- They cannot be proved congruent with the given information: This may apply if there is insufficient information to apply any congruence theorem.
Based on your question alone, I cannot definitively identify which theorem can be applied without specifics about the triangles (such as given angles or sides). Please provide more details for a more specific answer.
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