The Triangle Angle Sum Theorem and AAS Congruence allow us to use which other triangle congruence theorem to prove the triangles are congruent?

Answer 1

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees. AAS (Angle-Angle-Side) Congruence states that if two angles and a non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent.

When using AAS, you can also apply the Angle-Side-Angle (ASA) Congruence theorem. ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Given that when you have two angles and a side (not necessarily the one between the angles), you can still derive the included angle and apply ASA, proving that triangles are congruent.

In summary, the AAS Congruence can lead to the use of the ASA Congruence Theorem for proving triangle congruence.