"given: in ∆abc, segment de is parallel to segment ac .. prove: bd over ba equals be over bc. the two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.. statement. reason. 1. segment de is parallel to segment ac. 1. given. 2. line segment ba is a transversal that intersects two parallel lines. 2. conclusion from statement 1. 3.. 3.. 4. ∡bde ≅ ∡bac. 4. reflexive property of equality. 5. ∆abc ~ ∆dbe. 5. angle-angle (aa) similarity postulate. 6.. 6.. "