https://file.aiquickdraw.com/mathbot/file/1729306251536v20vf0om.jpg

To solve the problem in your image, let's walk through the **AAS Theorem**.

### AAS (Angle-Angle-Side) Theorem:
Two triangles are congruent if **two angles and the non-included side** in one triangle are congruent to two angles and the corresponding non-included side of another triangle.

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### Step-by-Step Analysis:
From the diagram, we have three triangles:

- **Triangle WXV**:  
  - A marked angle at \( W \)  
  - A marked angle at \( V \)  
  - A marked side \( \overline{WV} \)  

- **Triangle KIJ**:  
  - A marked angle at \( K \)  
  - A marked angle at \( J \)  
  - A marked side \( \overline{KI} \)  

- **Triangle DEF**:  
  - A marked angle at \( D \)  
  - A marked angle at \( F \)  
  - A marked side \( \overline{DE} \)  

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### Identifying Congruent Triangles:
To apply the AAS Theorem, look for two triangles with the **same angles and the corresponding side** between the same positions.

- **Triangle WXV** and **Triangle KIJ**:
  - Angle \( W \) matches with Angle \( K \) (single arc).  
  - Angle \( V \) matches with Angle \( J \) (double arc).  
  - Side \( \overline{WV} \) matches with Side \( \overline{KI} \).

Thus, **Triangle WXV ≅ Triangle KIJ** by the **AAS Theorem**.

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### Final Answer:
The two congruent triangles by the AAS theorem are:
\[
\boxed{WXV \cong KIJ}
\]

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Do you have any other questions, or would you like a deeper explanation?  

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### Related Questions:
1. What are the other triangle congruence theorems besides AAS?
2. How does AAS differ from the ASA theorem?
3. Can triangles be congruent by only angle-angle (AA)?
4. How can we prove two triangles are similar instead of congruent?
5. What is the significance of corresponding parts in congruent triangles?

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**Tip:** Always ensure that the matching sides in the triangles correspond correctly when applying any triangle congruence theorem.

Which two triangles are congruent by the AAS Theorem? Complete the congruence statement.

Learn how to identify congruent triangles using the AAS Theorem. This problem involves understanding triangle congruence criteria where two angles and the non-included side are congruent. Suitable for students in Grades 8-10.

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