https://file.aiquickdraw.com/mathbot/file/17280100937936lk1x7zz.jpg

The image presents a geometry problem with the following information:

**Given:**
- \( PQ = QR \)
- \( QR = 14 \)
- \( PR = 14 \)

**To Prove:** \( PQ = PR \)

### Solution:

1. We are given that \( QR = 14 \) and \( PR = 14 \). Since \( QR = PQ \) (given in the problem), we can replace \( QR \) with \( PQ \). Thus, we now have:

   \[
   PQ = PR = 14
   \]

2. Therefore, by substitution, \( PQ = PR \), which completes the proof.

### Conclusion:
This proves that \( PQ = PR \), as required.

Would you like further explanation or more details on this proof?

Here are some related questions for further understanding:
1. What is the significance of congruent line segments in geometry?
2. How can you use the properties of triangles to establish relationships between sides?
3. What types of triangles have two equal sides, as in this case?
4. How do substitution methods help in solving geometric proofs?
5. What are other common properties that can be used in triangle congruence problems?

**Tip:** In geometric proofs, always look for congruent sides or angles as key indicators for proving relationships between elements.

Given PQ = QR, QR = 14, PR = 14. Prove PQ = PR.

This problem involves proving that PQ equals PR given that PQ equals QR and both QR and PR are 14. It uses the substitution property of equality to show the equality of line segments. Suitable for students in Grades 6-8 learning basic geometric proof techniques.

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