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.

Question

What theorem has Patamon justified through this process?

A. the SSS Congruence Theroem
B. the SAS Congruence theorem
C. the CPCTC Theorem
D. the HL Congruence Theorem

Answer 1

Patamon has justified the SAS Congruence Theorem. The SAS (Side-Angle-Side) Congruence Theorem states that if two triangles have two pairs of corresponding sides that are congruent and the included angle between those sides is also congruent, then the triangles are congruent.

In this case, since Patamon demonstrated that a sequence of rigid transformations can map one triangle onto the other with one pair of congruent angles and two pairs of congruent sides, it confirms that the triangles are congruent according to the SAS Congruence Theorem.

Therefore, the correct answer is:

B. the SAS Congruence theorem