https://file.aiquickdraw.com/mathbot/file/1724775505870tddt9j4w.jpg

what is the congruence statement for these triangles? 1. AAS 2. SSS 3. ASA 4. SAS

To determine the congruence statement for the triangles in the second image, let's carefully examine the given information on the triangles.

### Analysis of the Image

The image shows two triangles with the following markings:

1. **First Triangle**:
   - Two sides are marked with a tick, indicating they are congruent.
   - An included angle between the marked sides is shown with an arc.

2. **Second Triangle**:
   - Two sides are also marked with the same tick, indicating these sides are congruent to those of the first triangle.
   - The included angle between these two sides is marked with the same arc.

### Matching the Given Congruence Criteria

Let's evaluate the options based on the analysis:

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

The triangles in the image have:
- Two pairs of congruent sides.
- One pair of congruent included angles.

This fits the **SAS (Side-Angle-Side)** congruence criterion, as both triangles have two sides and the angle between those sides congruent.

### Answer

The correct congruence statement for these triangles is:

**4. SAS (Side-Angle-Side)**

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

Here are some related questions to consider:

1. How do you prove two triangles are congruent using the AAS criterion?
2. What are some real-life applications of triangle congruence?
3. How can you determine if two triangles are congruent using the SSS criterion?
4. What is the difference between ASA and SAS congruence criteria?
5. Can triangles be congruent if they have the same area but different side lengths?

**Tip:** Remember, for the SAS congruence criterion, the angle must be the one between the two sides you are comparing.

Learn how to determine the congruence of triangles using AAS, SSS, ASA, and SAS criteria. Detailed analysis and examples provided. Suitable for high school students studying geometry.

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