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To determine if triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent based on the diagram, let's analyze the given information:

1. Both triangles have a right angle (\( \angle ACB \) and \( \angle DFE \)), as indicated by the right-angle symbols in each triangle.
2. The hypotenuses (\( AB \) in \( \triangle ABC \) and \( DE \) in \( \triangle DEF \)) are marked with congruent lines, suggesting that \( AB = DE \).

For right triangles, congruence can be established by the **Hypotenuse-Leg (HL) Congruence Theorem**, which states that two right triangles are congruent if they have congruent hypotenuses and one congruent leg. However, we are only given information about the hypotenuses, with no indication that a leg is congruent between the two triangles.

### Conclusion:
Without confirmation that one of the legs in \( \triangle ABC \) and \( \triangle DEF \) are congruent, we cannot conclude that the triangles must be congruent.

**Answer: B. False**

Would you like further clarification on this solution or the concepts involved?

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Here are 5 additional questions related to this topic:

1. What other criteria could we use to determine the congruence of two right triangles?
2. Can two triangles with equal hypotenuses and angles be similar instead of congruent?
3. What is the Hypotenuse-Leg (HL) Theorem, and when is it applicable?
4. How would we prove the congruence of two triangles if we know both their legs are equal?
5. How does the Pythagorean Theorem relate to proving triangle congruence?

**Tip:** Always check if any additional markings or information is provided when determining triangle congruence, as congruence theorems require specific criteria to be met.

Based on the information marked in the diagram, \( \triangle ABC \) and \( \triangle DEF \) must be congruent. True or False?

Explore how to determine the congruence of right triangles \( \triangle ABC \) and \( \triangle DEF \) based on the HL Congruence Theorem. This problem analyzes key geometric concepts and congruence criteria, perfect for students in Grades 8-10.

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