Explain how the angle-angle-side congruence theorem is an extension of the angle-side-angle congruence theorem. Be sure to discuss the information you would need for each theorem.

ASA congruence theorem: If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

AAS congruence theorem: If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Consider two triangles ΔABC and ΔA'B'C' . If AB=A'B', m∠A=m∠A' and m∠B=m∠B', then two triangles ΔABC and ΔA'B'C' are congruent by ASA theorem. 
 Now find ∠C and ∠C': 
 and . 
You have AB=A'B', m∠A=m∠A' , m∠C=m∠C' and that is the condition of AAS congruence theorem. These thoughts show you that AAS theorem is straight extension of ASA theorem.