Final answer:
Step 2 of the geometric proof likely involves the congruence of corresponding angles or alternate interior angles due to a line intersecting two sides of a triangle and being parallel to the third side.
Step-by-step explanation:
The question revolves around a geometric proof involving a line parallel to one side of a triangle intersecting the other two sides, and the focus is on identifying the reasoning behind a particular step in the proof. Specifically, the second step of this proof seems to involve the relationship between angles created when a line intersects two sides of a triangle. If the proof is following the properties of parallel lines and triangles, the likely reason justifying this step usually involves the congruence of angles, such as corresponding angles or alternate interior angles. In the context of triangles and parallel lines, when a line is parallel to a side of a triangle and intersects the other two sides, the created angles on each side of the intersecting line are congruent to the corresponding angles on the parallel side.
For example, in the context of Step 2 from the initial problem, if the line parallel to one side of the triangle is creating angles with the intersecting sides, then by the properties of parallel lines those angles could be corresponding or alternate interior angles, which are congruent due to the parallel nature of the lines. This fact is fundamental to proving that the segments are divided proportionally, which leads to the concept of similar triangles.