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 transformation map one triangle onto the other triangle such that the triangle overlap perfectly. What theorem had Peter justified through this process?

Question

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

Answer 1

Peter justified the SAS Congruence Theorem through this process. 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. In this case, Peter evidenced that the congruent angles between the congruent sides lead to the conclusion of triangle congruence through the series of transformations, which aligns with the SAS postulate.

Thus, the correct answer is: b. The SAS Congruence Theorem.