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.

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 $\overline{DE}$

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.

Final Answer:

The two congruent triangles by the AAS theorem are: $\boxed{WXV \cong KIJ}$

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

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?

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