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The diagram shows two right triangles, \( \triangle HIJ \) and \( \triangle KLM \), and we are asked which congruence theorems or postulates could be used to prove that \( \triangle HIJ \cong \triangle KLM \). Let's analyze the diagram and the options:

1. **Right Triangles**: Both triangles have right angles at \( \angle H \) and \( \angle K \). 
2. **Shared Angles**: Both triangles share similar orientation and structure, which suggests the presence of congruent sides or angles.
3. **Side Lengths**: The side \( HJ \) corresponds to \( KM \), and \( HI \) corresponds to \( KL \), making them candidates for congruent sides.

Now, let's examine the given congruence postulates:
- **A (ASA - Angle-Side-Angle)**: This requires two angles and the included side to be congruent. Since only one angle (the right angle) is given, this is not applicable.
- **B (LA - Leg-Angle)**: This is a valid criterion for right triangles, as one angle (the right angle) and one leg are given. This could work if the leg is congruent.
- **C (HA - Hypotenuse-Angle)**: If the hypotenuse and one angle are congruent, the triangles would be congruent. This could be applied if we are given that the hypotenuses are congruent.
- **D (AAS - Angle-Angle-Side)**: We need two angles and a non-included side, but since only one angle (the right angle) is known, this option isn't valid.
- **E (LL - Leg-Leg)**: This postulate is valid for right triangles if both legs are congruent, which seems applicable here based on the diagram.
- **F (HL - Hypotenuse-Leg)**: This is another valid criterion for right triangles if the hypotenuse and one leg are congruent.

### Correct answers:
- **B (LA)**
- **C (HA)**
- **E (LL)**
- **F (HL)**

Let me know if you'd like further clarification or details! 

Here are 5 related questions to explore the topic further:
1. What are the conditions for the Angle-Side-Angle (ASA) congruence postulate?
2. How can you prove triangles congruent using the Side-Angle-Side (SAS) postulate?
3. What is the difference between Leg-Angle (LA) and Hypotenuse-Angle (HA) in right triangles?
4. How do you apply the Hypotenuse-Leg (HL) theorem to prove triangle congruence?
5. What are the differences between LL and HL theorems for right triangles?

**Tip**: Always remember that for right triangles, special congruence theorems like HL and LL are applicable, unlike in other triangles.

Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why ∆HIJ ≅ ∆KLM? Check all that apply.

Discover which congruence theorems and postulates can be used to prove that ∆HIJ ≅ ∆KLM. This problem focuses on right triangle congruence, exploring ASA, LA, HA, AAS, LL, and HL theorems. Suitable for students in Grades 9-10.

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