If `Delta ABC ~= Delta PQR`, then which of the following is true ?

Options

A. AB = PR, BC = QR, AC = PQ
B. AB = PQ, BC = QR, AC = PR
C. AB = PR, AC = PQ BC = PR
D. None of these

Answer

To solve the problem, we need to understand the properties of congruent triangles. Given that triangle ABC is congruent to triangle PQR (denoted as ΔABC ≅ ΔPQR), we can establish the relationships between their corresponding sides.

### Step-by-Step Solution:

1. **Understanding Congruence**: When two triangles are congruent, it means that their corresponding sides and angles are equal. In this case, we have ΔABC ≅ ΔPQR.

2. **Identifying Corresponding Parts**: From the congruence of the triangles, we can identify the corresponding sides:
- Side AB corresponds to side PQ.
- Side AC corresponds to side PR.
- Side BC corresponds to side QR.

3. **Writing the Equalities**: Based on the correspondence:
- AB = PQ
- AC = PR
- BC = QR

4. **Evaluating Options**: Now, we need to check the options given in the question to find which statements are true based on the relationships we established:
- If an option states AB = PQ, it is true.
- If an option states AC = PR, it is true.
- If an option states BC = QR, it is true.
- If an option states AB = PR, it is false.

5. **Conclusion**: After evaluating the options, we can conclude that the correct relationships based on the congruence of the triangles are:
- AB = PQ
- AC = PR
- BC = QR

### Final Answer:
The correct relationships derived from the congruence of triangles ΔABC and ΔPQR are:
- AB = PQ
- AC = PR
- BC = QR