If three parallel lines intersect two transversals, then they divide the transversals proportionally.

A Corollary

If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides.

A Theorem

If 2 angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

A Postulate

If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar