https://file.aiquickdraw.com/mathbot/file/1726499413301h8c0i6x7.jpg

The image shows three triangles, and we are asked to determine which two triangles are congruent using the **SAS Theorem**. The **SAS (Side-Angle-Side) Congruence Theorem** states that if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, the triangles are congruent.

### Let's analyze the triangles:

1. **Triangle \( \triangle VWU \):**
   - \( \overline{VW} \) is marked congruent to \( \overline{EF} \).
   - The angle \( \angle VWU \) is congruent to \( \angle EFG \).
   - The side \( \overline{WU} \) is congruent to \( \overline{FG} \).

2. **Triangle \( \triangle EFG \):**
   - \( \overline{EF} \) is congruent to \( \overline{VW} \).
   - \( \angle EFG \) is congruent to \( \angle VWU \).
   - \( \overline{FG} \) is congruent to \( \overline{WU} \).

Thus, the two triangles that are congruent by the SAS theorem are \( \triangle VWU \) and \( \triangle EFG \).

### The congruence statement is:

\[
\triangle VWU \cong \triangle EFG
\]

Would you like more details or have any questions? Here are some related questions:

1. What other theorems can be used to prove triangle congruence?
2. Can the ASA (Angle-Side-Angle) theorem apply here as well?
3. What does the term "included angle" mean in triangle congruence?
4. How does the SAS theorem differ from the SSS (Side-Side-Side) theorem?
5. What are the properties of congruent triangles?

**Tip:** When identifying congruent triangles, always ensure that the sides and angles being compared are in corresponding positions.

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

This problem asks students to identify two congruent triangles using the SAS (Side-Angle-Side) theorem. It covers key geometry concepts, focusing on triangle congruence criteria and understanding of corresponding sides and angles.

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