Peter was given two generic triangles with one pair of congruent angles between two pairs of congruent sides. They show that a sequence of ridge transformations map one triangle onto the other triangle such that the triangles overlap perfectly. What theorem had Peter justified through this process?

Question

a. The HL Congruence Theorem
b. The SSS Congruence Theorem
c. The CPCTC Theorem
d. The SAS Congruence Theorem

Answer 1

Peter justified the SAS Congruence Theorem through this process. The SAS (Side-Angle-Side) Congruence Theorem states that if two triangles have two pairs of congruent sides and the angle between those sides is congruent, then the triangles are congruent. Since the triangles had one pair of congruent angles between two pairs of congruent sides, this setup aligns perfectly with the conditions of the SAS theorem.

Therefore, the correct answer is:

d. The SAS Congruence Theorem