This worksheet focuses on the AAS (Angle-Angle-Side) Triangle Congruence Theorem. This theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent.

Analysis of the Responses:

1. Problem 1:

   • The response states "Yes," indicating there is enough information for congruency.
   • Theorem: AAS (correctly identified).
   • Congruence Statement: $\triangle ABC \cong \triangle DEF$ (correctly written).
   • This answer is correct based on the information given, as two angles and one non-included side of each triangle are congruent.

2. Problem 2:

   • The response also states "Yes," confirming there is enough information for congruency.
   • Theorem: AAS (correctly identified).
   • Congruence Statement: $\triangle ABC \cong \triangle FED$.
   • This answer is correct as well, provided the two angles and the non-included side of each triangle are congruent.

The worksheet seems accurate and correctly follows the AAS Congruence Theorem. Each answer correctly identifies whether the triangles are congruent and provides an appropriate congruence statement.

Would you like more detailed explanations of the AAS theorem or the steps to validate congruence?

Follow-Up Questions

1. What is the difference between AAS and ASA (Angle-Side-Angle) congruence criteria?
2. How do you identify the non-included side in a triangle for AAS?
3. Can you use the AAS theorem if only one pair of angles is known to be congruent?
4. What are other triangle congruence theorems besides AAS and ASA?
5. How would you prove that two triangles are congruent if they share a side?

Tip

When identifying congruent parts in triangles, always ensure that the order of vertices in the congruence statement matches the corresponding angles and sides.