Patamon was given two generic triangles with one pair of congruent angles between two pairs of congruent sides. They show that a sequence of rigid transformations maps one triangle onto the other triangle such that the triangles overlap perfectly. What theorem has Patamon justified through this process? (1 point)

Question

1. the SSS Congruence Theorem

2. the CPCTC Theorem

3. the HL Congruence Theorem

4. the SAS Congruence Theorem

Answer 1

Patamon has justified the SAS Congruence Theorem through the process of showing that a sequence of rigid transformations maps one triangle onto the other such that the triangles overlap perfectly. The SAS (Side-Angle-Side) Congruence Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Since there is a pair of congruent angles between the pairs of congruent sides, this scenario corresponds to the SAS condition.

So, the answer is:

4. the SAS Congruence Theorem