Final answer:
The question involves a geometric proof in which the student seeks to prove two sides of a triangle are congruent given that two angles are congruent, applicable to the study of isosceles triangles and the base angles theorem.
Step-by-step explanation:
The question revolves around a mathematical proof process, specifically in geometric terms related to angles and sides of triangles. In this case, Nina is given that ∠OLN ≅ ∠LNO, which sounds like given angles of a triangle, and she wants to prove that OL ≅ ON, indicating she's trying to prove the sides opposite those angles are congruent. This falls under the concept of an isosceles triangle, where two angles are congruent and thus their opposite sides are also congruent. She could use properties of isosceles triangles or perhaps the base angles theorem to work through this proof. The context of the problem does not correspond with the content of the excerpts provided, which pertain to different subjects, such as Chemistry and Physics.