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Let's analyze each pair of triangles and determine if they are congruent using the appropriate criteria (SSS, SAS, ASA, AAS, HL, or not congruent):

### Problem 33:
- The triangles share two sides marked as congruent.
- Both triangles have a right angle (indicated by the square marking).
- Using the **Hypotenuse-Leg (HL)** criterion, these triangles are congruent because they are right triangles, and we have the hypotenuse and one leg congruent.

### Problem 34:
- There are three pairs of sides marked as congruent.
- This fits the **Side-Side-Side (SSS)** criterion for congruence. The triangles are congruent by SSS.

### Problem 35:
- There are two pairs of sides congruent, and the included angle between them is also congruent.
- This satisfies the **Side-Angle-Side (SAS)** criterion. The triangles are congruent by SAS.

### Problem 36:
- There are two angles marked congruent, and the included side between them is congruent.
- This fits the **Angle-Side-Angle (ASA)** criterion for congruence. The triangles are congruent by ASA.

### Problem 37:
- Only two angles are marked congruent, and a side opposite one of those angles is congruent.
- This satisfies the **Angle-Angle-Side (AAS)** criterion. The triangles are congruent by AAS.

### Problem 38:
- The two triangles share a right angle, and one leg and the hypotenuse are marked as congruent.
- This fits the **Hypotenuse-Leg (HL)** criterion for right triangle congruence. The triangles are congruent by HL.

If you need more details or have any questions, feel free to ask! Here are five related questions to extend your understanding:

1. What is the difference between ASA and AAS criteria for triangle congruence?
2. How does the Hypotenuse-Leg (HL) theorem work for right triangles?
3. Can two triangles be congruent if they share only two pairs of congruent angles?
4. In triangle congruence, why is the included side or angle important for certain criteria?
5. What are the conditions under which triangles are not congruent?

**Tip:** Always check if the triangles are right triangles when working with the Hypotenuse-Leg (HL) criterion for congruence.

Determine if each pair of triangles is congruent. Write SSS, SAS, ASA, AAS, HL, or not congruent.

Analyze six triangle pairs to determine their congruence using SSS, SAS, ASA, AAS, or HL. This problem involves identifying congruence in right and non-right triangles using key congruence criteria such as Side-Side-Side, Side-Angle-Side, and Hypotenuse-Leg for right triangles.

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