Prove that a lie divides two sides of a triangle proportionally is parallel to the third side. be sure to create and name the appropriate geometric figures.

Congruence between two triangles means six items, all three sides and all three angles, are congruent. Thus the statement ABC DEF has a very precise meaning. It succinctly summarizes the six statements (assume lines atop these segments): ABDE, BCEF, ACDF, AD, BE, and CF. It is very important to maintain the vertices in the proper order. Not doing so is a common mistake.