Patagonia was given two generic triangles with one pair of congruent angles between two pairs of congruent sides. They show that a sequence of rigid transformation maps one triangle onto the other triangle such that the triangles overlap perfectly. What theorem has Patamon justified through this process?

Question

GPT-4o mini · Answer

Patagonia has justified the **Angle-Angle-Side (AAS) Congruence Theorem** through the process of demonstrating that a sequence of rigid transformations can map one triangle onto another such that they overlap perfectly. In the scenario described, they have two triangles with one pair of congruent angles and two pairs of congruent sides. Since the triangles have two angles and the included side (one pair of congruent angles and the side between them) congruent, this satisfies the conditions of the AAS theorem, leading to the conclusion that the triangles are congruent.