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.