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 though this process?

Question

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 though this process?
A. the SAS congruence theorem 
B. the HL congruence theorem 
C. the SSS congruence theorem
D. the CPCTC theorem

GPT-4o mini · Answer

Patamon's process of showing that a sequence of rigid transformations maps one triangle onto another, given a pair of congruent angles between two pairs of congruent sides, justifies the SAS congruence theorem.

Therefore, the correct answer is: A. the SAS congruence theorem.

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.