https://file.aiquickdraw.com/mathbot/file/173041066841005uy2aog.jpg

To answer this question, let's analyze the congruence theorems available and determine which one applies based on the image provided.

The question asks: **What triangle congruence theorem could you use to prove these triangles congruent?** The answer choices are:
1. SSS (Side-Side-Side)
2. SAS (Side-Angle-Side)
3. ASA (Angle-Side-Angle)
4. AAS (Angle-Angle-Side)

### Analysis
The image shows two triangles within a larger triangle, sharing a common side. There is also an angle marking, indicating the two triangles have a pair of congruent angles. To determine the correct theorem:

- **SSS (Side-Side-Side)**: This would require all three pairs of corresponding sides of the triangles to be congruent. 
- **SAS (Side-Angle-Side)**: This requires two pairs of corresponding sides and the included angle between them to be congruent.
- **ASA (Angle-Side-Angle)**: This requires two pairs of corresponding angles and the side between them to be congruent.
- **AAS (Angle-Angle-Side)**: This requires two pairs of corresponding angles and a non-included side to be congruent.

Based on the marking in the image, it looks like the **SAS (Side-Angle-Side)** theorem would be most appropriate, as there is a common side and a pair of congruent angles. 

### Conclusion
The correct answer is likely **SAS (Side-Angle-Side)**.

Would you like further details on the SAS theorem or have any questions?

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### Related Questions
1. How does the SSS theorem differ from the SAS theorem in proving congruence?
2. What additional information would be required to use the ASA theorem?
3. How is the common side in congruent triangles important for the proof?
4. Could we use the AAS theorem in any scenario with this diagram?
5. Why are congruent triangles useful in geometry proofs?

### Tip
Remember, identifying shared sides or angles in diagrams can help quickly determine applicable congruence theorems.

What triangle congruence theorem could you use to prove these triangles congruent?

Learn about triangle congruence theorems to determine if two triangles are congruent. Explore different methods like SSS, SAS, ASA, and AAS and understand how to identify the appropriate theorem using diagram markings. This topic is suitable for students in Grades 8-10 studying geometry.

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