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The image contains a worksheet asking to determine if pairs of triangles can be proven congruent using congruence theorems like **SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or HL (Hypotenuse-Leg)**. I will analyze each pair of triangles step by step and determine the correct theorem for congruence where possible.

Here is my breakdown:

1. **Problem 1**: 
   - The triangles share two sides of equal length and a common angle.
   - **Conclusion**: They can be proven congruent by **SAS**.

2. **Problem 2**:
   - There are two pairs of corresponding sides marked congruent, but no angles are given.
   - **Conclusion**: Insufficient information to prove congruence. No theorem applies.

3. **Problem 3**:
   - Two angles and one side are marked congruent.
   - **Conclusion**: The triangles are congruent by **AAS**.

4. **Problem 4**:
   - One pair of right angles and two sides are marked congruent.
   - **Conclusion**: The triangles are congruent by **HL** (Hypotenuse-Leg, for right triangles).

5. **Problem 5**:
   - Three sides of each triangle are congruent.
   - **Conclusion**: The triangles are congruent by **SSS**.

6. **Problem 6**:
   - Two angles and the included side are congruent.
   - **Conclusion**: The triangles are congruent by **ASA**.

7. **Problem 7**:
   - The triangles share two angles and one side.
   - **Conclusion**: The triangles are congruent by **AAS**.

8. **Problem 8**:
   - No congruent angles or sides are indicated.
   - **Conclusion**: Insufficient information to determine congruence.

9. **Problem 9**:
   - The triangles have a right angle and two pairs of congruent sides.
   - **Conclusion**: The triangles are congruent by **HL**.

10. **Problem 10**:
    - There are two pairs of corresponding sides and an included angle.
    - **Conclusion**: The triangles are congruent by **SAS**.

11. **Problem 11**:
    - Two angles and a side are marked congruent.
    - **Conclusion**: The triangles are congruent by **AAS**.

12. **Problem 12**:
    - Three sides of each triangle are congruent.
    - **Conclusion**: The triangles are congruent by **SSS**.

Would you like more details on any specific problem, or have any questions about congruence theorems?

Here are 5 related questions:
1. What is the difference between the **SAS** and **ASA** theorems?
2. How does the **HL** theorem apply to right triangles?
3. Can triangles be congruent if only two angles are known, without sides?
4. What additional information would be needed to determine congruence in Problem 2?
5. Why doesn't Problem 8 have enough information to prove congruence?

**Tip**: Always look for corresponding pairs of sides and angles when determining congruence. Matching an angle or side incorrectly can lead to wrong conclusions!

Compare the triangles and determine whether they can be proven congruent, if possible, by SSS, SAS, ASA, AAS, or HL.

This problem focuses on proving the congruence of triangles using various congruence theorems such as SSS, SAS, ASA, AAS, and HL. Suitable for students in grades 8-10, this geometry worksheet covers congruence rules step by step.

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