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It is necessary to write the corresponde...

It is necessary to write the correspondence of vertices correctly for writing congruence of triangles in symbolic form .

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To determine whether the statement "It is necessary to write the correspondence of vertices correctly for writing the congruence of triangles in symbolic form" is true or false, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding Congruence of Triangles**: - Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal. 2. **Identifying Corresponding Vertices**: - When we denote two triangles, we label their vertices. For example, let’s consider triangle ABC and triangle PQR. Here, A corresponds to P, B corresponds to Q, and C corresponds to R. 3. **Using the SSS Criterion**: - If we know that the sides of triangle ABC are equal to the sides of triangle PQR (i.e., AB = PQ, BC = QR, and AC = PR), we can say that triangle ABC is congruent to triangle PQR by the Side-Side-Side (SSS) criterion. 4. **Writing the Congruence Statement**: - The correct way to express the congruence of these triangles symbolically is: \[ \triangle ABC \cong \triangle PQR \] - This notation indicates that the corresponding parts of these triangles are equal. 5. **Importance of Correct Correspondence**: - If we write the congruence incorrectly, for example, stating that triangle ABC is congruent to triangle RQP, we would misrepresent the relationships between the sides and angles. This could lead to incorrect conclusions about which sides and angles are equal. 6. **Conclusion**: - Therefore, it is indeed necessary to write the correspondence of vertices correctly when expressing the congruence of triangles in symbolic form. The statement is **true**.
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