https://file.aiquickdraw.com/mathbot/file/172605987022666t21xzp.jpg

The question asks whether triangles \(\triangle XYZ\) and \(\triangle ABC\) must be congruent based on the information provided in the diagram.

### Key Observations:
- Both triangles are right-angled at vertices \(Z\) and \(C\), respectively.
- Both diagrams show one leg of the triangles (marked) as congruent: \(XZ \cong AC\).
- However, no additional information is provided about the other sides or angles.

### Conclusion:
For triangles to be congruent, we need to satisfy one of the congruence criteria such as:
1. **SSS** (Side-Side-Side)
2. **SAS** (Side-Angle-Side)
3. **ASA** (Angle-Side-Angle)
4. **AAS** (Angle-Angle-Side)
5. **HL** (Hypotenuse-Leg for right triangles)

In this case, only one side and the right angle are marked as congruent. Without more information about the second side or angles, we cannot definitively conclude that these triangles are congruent. Thus, the statement that the triangles must be congruent is **False**.

### Correct Answer: 
**B. False**

Would you like more details on triangle congruence criteria?

Here are some related questions:
1. What are the different triangle congruence theorems?
2. Can two triangles be congruent if only one side is known to be equal?
3. How does the Hypotenuse-Leg (HL) theorem work in congruence?
4. What is the difference between congruent and similar triangles?
5. How does the Side-Angle-Side (SAS) criterion apply to right triangles?

**Tip**: When solving triangle congruence problems, always look for at least two corresponding sides or angles in addition to any right angle, to apply a valid congruence theorem.

Based on the information marked in the diagram, must triangles XYZ and ABC be congruent?

This problem explores whether triangles XYZ and ABC must be congruent based on the given geometric diagram. Key concepts include triangle congruence theorems such as Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Hypotenuse-Leg (HL). Suitable for students in Grades 8-10.

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