Final answer:
Triangles may be similar by AA~, SSS~, or SAS~ criteria. The triangles in question, BAO and B₁A₁O, satisfy one of these criteria, suggesting they are similar and corresponding sides are proportional.
Step-by-step explanation:
To determine whether the triangles are similar, we can use the criteria of AA~ (Angle-Angle Similarity), SSS~ (Side-Side-Side Similarity), or SAS~ (Side-Angle-Side Similarity). Similarity by AA~ requires that two angles of one triangle are congruent to two angles of another triangle. SSS~ requires that all three sides of one triangle are proportional to the corresponding sides of another triangle. SAS~ means that two sides of one triangle are proportional to two sides of another triangle, and the included angles are congruent.
The question suggests that triangles BAO and B₁A₁O are similar; thus, we can infer that they satisfy one of the similarity conditions mentioned above. If this is known, then the corresponding sides are proportional, leading to a similarity statement such as ∆BAO ≅ ∆B₁A₁O, indicating that triangle BAO is similar to triangle B₁A₁O.