Subjects geometry

Triangle Congruence 5C3A20

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1. The problem asks to identify the postulate that makes the two triangles congruent based on the given markings. 2. The left triangle has a marked side TS and an angle at R. 3. The right triangle has a marked side AB and two angles at C and B. 4. To determine congruence, we look for matching parts: sides and angles. 5. The postulates for triangle congruence include: - SAS (Side-Angle-Side): Two sides and the included angle are congruent. - ASA (Angle-Side-Angle): Two angles and the included side are congruent. - AAS (Angle-Angle-Side): Two angles and a non-included side are congruent. 6. Here, the left triangle has one side (TS) and one angle (R), while the right triangle has one side (AB) and two angles (C and B). 7. Since the right triangle has two angles marked and the left triangle has one angle and one side marked, the best match is AAS (Angle-Angle-Side), where two angles and a side (not necessarily included) are congruent. 8. Therefore, the postulate that makes the triangles congruent is AAS. Final answer: AAS