Jared was given two generic triangles with a pair of congruent sides between two pairs of congruent angles. He shows that a sequence of rigid transformations maps one triangle onto the other triangle such that the triangles overlap perfectly. What theorem has he justified through this process?

Answer 1

Jared has justified the Side-Angle-Side (SAS) Congruence Theorem through his process. The SAS Theorem states that if two triangles have a pair of congruent sides and the angles included between these sides (between the two congruent sides) are also congruent, then the triangles are congruent. Since he demonstrated that a sequence of rigid transformations can map one triangle onto the other so that they overlap perfectly, it confirms that the two triangles are indeed congruent by the SAS Congruence Theorem.