The document discusses several theorems related to proportionality in triangles: - The side-splitter theorem states that a line parallel to one side of a triangle divides the other two sides proportionally. - The triangle proportionality theorem can be used to verify if two segments are parallel. - The two transversal proportionality corollary states that two or more parallel lines divide two transversals proportionally. - The triangle angle bisector theorem states that if a ray bisects an angle of a triangle, it divides the opposite side into segments proportional to the other two sides. Examples are provided to demonstrate applying these theorems.