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.

Answer:

The AAS congruence theorem is considered an extension of the ASA theorem because of the Triangle Angle Sum Theorem, which states that the interior angles of a triangle sum to 180 degrees. If you are given two angles and a non-included side (AAS), you can subtract the sum of the two known angles from 180 to find the third angle. Once you have the third angle, the given side becomes the included side between two known angles, effectively converting the AAS information into ASA information.