To determine the appropriate theorem for proving triangles congruent, we need to consider the specific information you have about the triangles. Here are the common congruence theorems:
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SSS (Side-Side-Side): If all three sides of one triangle are equal to all three sides of another triangle, the triangles are congruent.
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SAS (Side-Angle-Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
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ASA (Angle-Side-Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
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AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are equal to two angles and a corresponding side of another triangle, the triangles are congruent.
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HL (Hypotenuse-Leg): Specifically for right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, the triangles are congruent.
If you provide the specific information about the triangles in question (e.g., which sides or angles are known), we can pinpoint which theorem applies. If the information is insufficient to establish any of the congruency conditions, then the response "Not Possible to prove congruency with the given information" may be applicable. Please provide the details for a more precise answer.
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