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To determine if the triangles \( WXZ \) and \( YXZ \) are congruent, let's analyze the given diagram and apply congruence postulates.

From the image:

1. **Shared Side:** Both triangles share the side \( XZ \).
2. **Vertical Angles:** The angle at \( X \) (where the two triangles meet) is congruent because it is the same angle for both triangles.
3. **Equal Sides:** \( WX = YX \), which is marked as congruent in the diagram.

Based on these observations, we have:
- One pair of sides congruent (\( WX = YX \)).
- A shared side (\( XZ = XZ \)).
- The included angle \( \angle WXZ = \angle YXZ \), as they are vertical angles.

These observations satisfy the **SAS (Side-Angle-Side)** criterion for triangle congruence. Thus, the correct answer is:

**B. The triangles are congruent by SAS.**

Would you like further details on congruence postulates or any other questions? Here are some additional questions to expand understanding:

1. What are the key differences between the SAS and ASA congruence postulates?
2. Can two triangles be congruent if they only share two angles but not a side?
3. How can the shared side help in proving triangle congruence?
4. Why are vertical angles always congruent?
5. In what cases would the AAS postulate apply instead of SAS?

**Tip:** Always look for shared sides and angles in diagrams, as they often provide clues for congruence proofs.

Determine whether the triangles must be congruent. If so, name the postulate or theorem that best justifies your answer. If not, explain.

Explore how to determine if two triangles are congruent using the SAS postulate. This problem involves identifying congruent sides and angles, applying the vertical angles theorem, and verifying triangle congruence with the SAS postulate. Suitable for students in Grades 8-10.

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