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.