To determine the appropriate theorem that proves the congruence of the two triangles based on the image description (which shows two congruent triangles), we can use the following information about the congruence theorems:
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SSS (Side-Side-Side) 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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SAS (Side-Angle-Side) Theorem: States that if two sides of one triangle and the angle between them are equal to two sides of another triangle and the angle between them, then the triangles are congruent.
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HL (Hypotenuse-Leg) Theorem: Specific to right triangles, this states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
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ASA (Angle-Side-Angle) 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 choose the correct theorem, you would need to look for evidence of sides or angles being equal between the two triangles. Without seeing the image, I cannot definitively choose one, but you should assess which properties (sides or angles) are given in your image to select the correct response.
If the two triangles demonstrate equal corresponding sides, the SSS Theorem is likely applicable. If it showcases two sides and the included angle being equal, then choose SAS Theorem. For right triangles, look for the HL Theorem, and if angles are involved with an included side, consider the ASA Theorem.
Please reference the specific properties of the triangles shown to make your selection!
5 answers