Answer
The proof is in the following form:
Column 1 of proof; Column 2 of proof.
Thus, we have:
1. The line is parallel to one of the other sides of the triangle; given.
2. The line creates a smaller triangle. The base angles of this smaller triangle are equal to the base angles of the larger triangle; when two parallel lines are intersected by the same transversal, corresponding angles are similar.
3. The large and smaller triangle are similar; AA similarity theorem
4. If the line bisects the first side, then it bisects the third side; corresponding parts of similar triangles are proportional.