Final answer:
To prove triangle similarity, the AA, SSS, or SAS postulates could be used, depending on whether two angles, three sides, or two sides and the included angle of the triangles are known to be congruent or proportional, respectively.
Step-by-step explanation:
To determine which similarity postulate or theorem applies to prove that two triangles are similar, we must examine the given information about the triangles. Since we are given that Triangles BAO and B₁A₁O are similar, the appropriate method would depend on the specific information pertaining to angles and sides of the triangles in question. For example, if we know that two angles of one triangle are congruent to two angles of another triangle, we would use the AA (Angle-Angle) similarity postulate. If all three corresponding sides are in proportion, we would use the SSS (Side-Side-Side) similarity postulate. Likewise, if two corresponding sides are in proportion and the included angle is congruent, we would use the SAS (Side-Angle-Side) similarity postulate. Without additional information about the sides or angles, we cannot definitively choose which postulate or theorem applies.