The problem in the image involves a triangle $\triangle PQR$ with the following information:

Given:

• $PQ \cong QR$
• $QR = 14$
• $PR = 14$

To Prove:

• $PQ \cong PR$

Proof:

1. Given:

   • $PQ \cong QR$ (it is stated in the problem)
   • $QR = 14$
   • $PR = 14$

2. Since $PR = 14$ and $QR = 14$, we can conclude that $PR \cong QR$ (they have the same length).

3. Also, we know from the given that $PQ \cong QR$. Therefore, we have $PQ \cong PR$ by the transitive property of equality (if two segments are both congruent to a third segment, they are congruent to each other).

Conclusion:

Thus, $PQ \cong PR$, as required.

Would you like further details or have any questions? Here are some follow-up questions:

1. How does the transitive property of equality work in geometry?
2. Can you explain why two sides of a triangle being equal make it isosceles?
3. How does the congruence of sides affect the angles in a triangle?
4. What is the difference between congruent and equal in geometry?
5. How does triangle congruence relate to similarity?

Tip: When working with geometric proofs, always keep properties like symmetry and transitivity in mind, as they help in proving congruence efficiently.