https://file.aiquickdraw.com/mathbot/file/1724775295638fjajxs7p.jpg

what’s the congruence statement of these triangles? 1. AAS 2. SSS 3. ASA 4. SAS

To determine the congruence statement of the two triangles shown in the image, we need to analyze the given information about the sides and angles of the triangles.

### Analysis of the Image

The image displays two triangles, each marked with three pieces of information (sides or angles):

1. **First Triangle**:
   - There are two angles marked with a single arc each.
   - There is one side marked between these two angles.

2. **Second Triangle**:
   - There are two angles marked with a single arc each, similar to the first triangle.
   - There is one side marked between these two angles, similar to the first triangle.

### Matching the Given Congruence Criteria

Let's evaluate the provided options:

1. **AAS (Angle-Angle-Side)**: Two angles and a non-included side are congruent.
2. **SSS (Side-Side-Side)**: All three sides are congruent.
3. **ASA (Angle-Side-Angle)**: Two angles and the included side are congruent.
4. **SAS (Side-Angle-Side)**: Two sides and the included angle are congruent.

### Conclusion

In both triangles:
- Two angles are marked congruent.
- The side between the two congruent angles is also marked as congruent.

This information matches the **ASA (Angle-Side-Angle)** congruence criterion because both triangles have two angles and the side between them marked congruent.

### Answer

The correct congruence statement for these triangles is:

**3. ASA (Angle-Side-Angle)**

Would you like more details on how to apply the ASA congruence criterion or have any questions?

Here are some related questions to consider:

1. What are the properties of congruent triangles?
2. How can you prove two triangles are congruent using the SAS criterion?
3. What is the difference between ASA and AAS congruence criteria?
4. How does the SSS criterion for triangle congruence work?
5. Can two triangles be congruent if they have three pairs of congruent angles?

**Tip:** When determining the congruence of triangles, pay close attention to the placement of congruent sides and angles to ensure the correct criterion is used.

Explore the criteria for triangle congruence including AAS (Angle-Angle-Side), SSS (Side-Side-Side), ASA (Angle-Side-Angle), and SAS (Side-Angle-Side). Learn how to apply these criteria with detailed examples and explanations.

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