Final answer:
To determine if triangles BAO and B₁A₁O are similar, we apply similarity postulates such as AA, SAS, and SSS. The correct postulate depends on the given angles and side lengths. HL Similarity is not a similarity postulate but a congruence theorem for right triangles.
Step-by-step explanation:
When comparing two triangles to ascertain if they are similar, there are a few criteria we can apply based on the information given. These are known as similarity postulates or theorems:
- AA Similarity - If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.
- SAS Similarity - If two sides of one triangle are proportional to two sides of another triangle, and the included angles are congruent, then the triangles are similar.
- SSS Similarity - If all three sides of one triangle are proportional to all three sides of another triangle, then the triangles are similar.
- HL Similarity does not exist for triangles since it is a criterion for congruence in right triangles known as Hypotenuse-Leg congruence.
In the given problem, you are essentially confirming the similarity of triangles BAO and B₁A₁O using one of the theorems mentioned above. The provided equations and values seem to hint towards the proportionality of the sides or the congruence of angles, which suggests AA, SAS, or SSS similarity could be at play here, although the actual criterion used would depend on the accurate data points given for these triangles.