Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which of the following is NOT a triangle theorem?

The correct answer is: SSA

The option that is determined not to be a triangle theorem is based on the properties and restrictions of triangle congruence criteria. The SSS (Side-Side-Side), SAS (Side-Angle-Side), and AAS (Angle-Angle-Side) criteria are all legitimate theorems used to establish congruence between triangles. In contrast, the SSA (Side-Side-Angle) condition does not guarantee congruence. This is due to the fact that two triangles can satisfy the side-side-angle condition yet not be congruent. An example of this is the "Ambiguous Case," which can occur with the Law of Sines when two different triangles can be constructed with the same dimensions. This lack of assurance makes SSA not a theorem for establishing congruence in triangles. Therefore, the selection of SSA as the option that is not a triangle theorem is based on its inability to consistently provide congruent results, unlike the other criteria which are universally accepted axioms in triangle geometry.