https://file.aiquickdraw.com/mathbot/file/1727209014284f0gj4ibp.jpg

To solve the proof, we are given the diagram of triangle \(WVZ\) with two internal points \(X\) and \(Y\) along segments \(WV\) and \(VZ\) respectively. Here’s the step-by-step breakdown of the proof:

**Given**: 
1. \(WX \cong YZ\)
2. \(VX \cong VZ\)

**To Prove**: 
- \(WY \cong XZ\)

### Proof

1. **Statement**: \(WX \cong YZ\)  
   **Reason**: Given.

2. **Statement**: \(VX \cong VZ\)  
   **Reason**: Given.

3. **Statement**: \(WV = WV\)  
   **Reason**: Reflexive property (a segment is congruent to itself).

4. **Statement**: \(\triangle WVX \cong \triangle WVZ\)  
   **Reason**: Side-Side-Side (SSS) congruence postulate (from steps 1, 2, and 3).

5. **Statement**: \(WY \cong XZ\)  
   **Reason**: Corresponding parts of congruent triangles (CPCTC).

### Conclusion:
Thus, \(WY \cong XZ\) is proven by the congruence of triangles and the corresponding parts.

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Would you like more details or have any questions on the proof? Here are 5 related questions you might want to explore:

1. How does the reflexive property help in proving triangle congruence?
2. What is the significance of the SSS congruence postulate?
3. How can we apply CPCTC in other triangle congruence proofs?
4. What other congruence postulates (like SAS or ASA) could work in this scenario?
5. How do we prove congruence in non-right triangles?

**Tip**: When proving triangle congruence, always look for shared sides or angles, as they often simplify the proof!

Prove that WY ≅ XZ, given WX ≅ YZ and VX ≅ VZ in triangle WVZ with internal points X and Y.

This proof demonstrates how to use the SSS congruence postulate and CPCTC to prove WY ≅ XZ, given WX ≅ YZ and VX ≅ VZ in a triangle. Ideal for students in grades 9-11 studying congruent triangles.

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