To determine which theorem proves that two triangles are congruent, we need to identify the properties of the triangles in question (like their sides and angles).
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HL Theorem (Hypotenuse-Leg Theorem): This theorem applies only to right triangles. It states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the triangles are congruent.
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SAS Theorem (Side-Angle-Side Theorem): This theorem states that if two sides of one triangle are equal to two sides of another triangle, and the angle formed between those sides is also equal, then the triangles are congruent.
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SSS Theorem (Side-Side-Side Theorem): This theorem states that if all three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.
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ASA Theorem (Angle-Side-Angle Theorem): This theorem states that if two angles and the side between them of one triangle are equal to two angles and the side between them of another triangle, then the triangles are congruent.
To determine the correct theorem, you would need specific information regarding the sides and angles of the triangles in question. If you know the configuration—such as whether the triangles are right triangles or have specific segment lengths or angle measurements—then you can select the appropriate congruence theorem.
Without additional details regarding the triangles in your question, I cannot definitively say which theorem proves their congruence. Please provide more information about the sides and angles of the triangles for a conclusive answer.