To determine the congruence theorem that makes the triangles equal, let's analyze the image provided:

• The triangles are labeled as triangle ABC (on the left) and triangle DEF (on the right).
• The two pairs of sides are marked with equal signs:
  • $AB = DE$
  • $AC = DF$
• Additionally, the angle at vertex A is equal to the angle at vertex D ($\angle A = \angle D$), indicated by the same mark at the vertices.

Based on this information, the congruence theorem that makes these two triangles equal is the Side-Angle-Side (SAS) Congruence Theorem. This theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Therefore, we can conclude:

• Congruence Theorem: SAS (Side-Angle-Side)
• ABC = DEF

Would you like further details or have any questions about this theorem?

Here are some related questions to explore:

1. What are the other congruence theorems besides SAS?
2. Can you prove the SAS congruence theorem using geometric constructions?
3. How would you use the SSA condition and why does it not always result in congruent triangles?
4. What is the importance of the "included angle" in the SAS theorem?
5. How would you determine triangle congruence using the SSS theorem?

Tip: Always remember that the included angle (the angle between the two given sides) is crucial for using the SAS congruence theorem.