Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which triangle congruence theorem uses the Side-Angle-Side property?

The correct answer is: SAS

The Side-Angle-Side (SAS) congruence theorem is specifically designed to determine the congruence of two triangles when two sides and the angle between them are known to be equal. When using the SAS theorem, if two sides of one triangle are equal to two sides of another triangle, and the included angle between those sides is also equal, then the two triangles are congruent. This method focuses on the fact that the specific arrangement of the sides and the included angle ensure that the shape and size of the triangles are preserved. The SAS theorem is particularly powerful because it provides a clear criterion that can be easily verified using measurements: checking two sides and the angle they form. In contrast, the other congruence theorems like ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side) rely on different combinations of angles and sides. Each of these theorems serves unique conditions under which triangles can be proven congruent, but SAS specifically emphasizes the importance of the relationship between two sides and the angle that connects them.