Carlos says that the XYZ is not congruent to PQR because there is no SSA theorem or postulate.
In two or more complete sentences, explain why or why not Carlos is correct. Justify your answer using triangle congruency postulates, theorems, and definitions.
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If the figure is showing all pairs of corresponding sides that are congruent and all pairs of corresponding angles that are congruent, an no other pairs of sides or angles are congruent, then Carlos is correct. Using the given congruent angles X and P, the pair of congruent sides XY and PQ, and the pair of congruent sides YZ and QR, corresponding sides XZ and PR must be of different lengths, so the triangles are not congruent.
On the other hand, if the figure shows some pairs of corresponding parts but not necessarily all, then Carlos is incorrect. Carlos stated that the triangles are not congruent. He is correct that there is no SSA theorem or postulate, so we do not have enough information to prove that the two triangles are congruent, but at the same time, we don't have information to prove they are not congruent. Since we have no information on another pair of sides or angles, we simply do not know if the triangles are congruent or not. We cannot conclude they are not congruent.
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