Final answer:
Without concrete information on the side lengths or angles of the triangles described, we cannot determine if they are congruent. The mention of HL, AAS, and ASA congruence criteria suggest a need for specific data that is not provided within the question, thus preventing a conclusion on congruency.
Step-by-step explanation:
When determining if two triangles are congruent, we rely on certain postulates such as SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles). To determine congruence, we must know specific information about the triangles in question, such as the lengths of sides and the measures of angles. Without that information, we cannot definitively determine congruence.
In the case of the provided information, it appears that the triangles being referenced do not give clear data to determine congruence. If we had concrete measurements or if the triangles shared specific sides or angles, then we could apply the congruence postulates. The HL theorem applies only to right triangles and it states that if the hypotenuse and one leg of a right triangle are equal to the corresponding parts of another right triangle, the two right triangles are congruent.
However, in your description, there's no clear indication that any of these postulates can be applied due to the lack of information. For instance, Triangles BAO and B₁A₁O, and Triangles NOF and B₁A₁F don't provide enough context or data to identify a specific postulate for congruence. Thus, based on the given details, we cannot conclude whether the triangles are congruent or not.
Still, the relation 'If a is more than b, and b is more than c, then a is more than c' is a known logical rule often referred to as the transitive property, which is used in mathematics to relate different terms in a sequence of inequalities. For specific triangle congruence postulates, we must have information related to side lengths or angles to utilize them effectively.