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.

Question: 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. 

In this blog post, I will explain how the angle-angle-side (AAS) congruence theorem is an extension of the angle-side-angle (ASA) congruence theorem. I will also discuss the information you would need for each theorem to prove that two triangles are congruent.

The ASA congruence theorem states that if two angles and the included side of one triangle are equal to the corresponding angles and the included side of the other triangle, then the triangles are congruent. The included side is the side between the two angles.

The AAS congruence theorem states that if two angles and the non-included side of one triangle are equal to the corresponding angles and the non-included side of the other triangle, then the triangles are congruent. The non-included side is the side that is not between the two angles, but adjacent to them.

The AAS theorem is an extension of the ASA theorem because it covers a case where the ASA theorem does not apply. For example, if we have two triangles ABC and DEF such that ∠A = ∠D, ∠B = ∠E, and BC = EF, we cannot use the ASA theorem to prove that they are congruent because BC and EF are not included sides. However, we can use the AAS theorem to prove that they are congruent because BC and EF are non-included sides.

The information you would need for each theorem is as follows:

- For ASA, you would need to know two angles and the included side of one triangle, and their corresponding parts in the other triangle.

- For AAS, you would need to know two angles and the non-included side of one triangle, and their corresponding parts in the other triangle.

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