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

CPCTC
SAS
HL

Answer 1

Jenny has justified the SAS (Side-Angle-Side) theorem through the process described. This theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the angles between those sides are congruent, then the two triangles are congruent. Since she demonstrated that a sequence of rigid transformations can map one triangle onto the other, it confirms their congruence based on the conditions of the SAS theorem.

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is typically used after establishing triangle congruence, so it does not specifically apply here. HL (Hypotenuse-Leg) is specific to right triangles, and since Jenny is dealing with generic triangles (not right triangles), this theorem would not apply either.

Thus, the correct answer is SAS.