Jenny was given two generic triangles (not right 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 Jenny justified through this process?

Question

A. CPCTC
B. SAS
C. HL

Answer 1

Jenny has justified the SAS (Side-Angle-Side) theorem through her process. The SAS theorem states that if two triangles have two pairs of congruent sides and the included angle between those sides is also congruent, then the triangles are congruent. In this case, since she has one pair of congruent angles between two pairs of congruent sides, it aligns with the conditions of the SAS theorem.

Here's a brief overview of the options:

• A. CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is a property used after proving two triangles are congruent.
• B. SAS is correct in this context, as it is the theorem that establishes the congruence based on the given conditions.
• C. HL (Hypotenuse-Leg) applies specifically to right triangles.

Therefore, the correct answer is B. SAS.