If a line is constructed parallel to one side of a triangle that intersects the other two sides in distinct points, then the other two sides each form a transversal where the corresponding angles are equal. Since you now have two triangles with two pairs of angles equal because of equal corresponding angles of a transversal and the third angle is in common, you have two triangles that have all three angles congruent. Since all three angles are congruent, the triangles must be similar (AAA). Since the triangles are similar, their corresponding sides are in proportion by definition of similarity.
