Question

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

Answer 1

@ranga Thanks again

Answer 2

Statement Reason
DB/AD = EC/AE Given (Line divides 2 sides
of a triangle proportionally)

DB/AD+1 = EC/AE+1 Addition Property of Equality
or (DB+AD)/AD = (EC+AE)/AE
or AB/AD = AC/AE

Included angle A = included Reflexive Property
angle A

Triangles ADE and ABC are SAS for Similarity Theorem.
similar

Angle ADE = Angle ABC Corresponding angles of similar triangles
are congruent.

DE is parallel BC Corresponding angles ADE and ABC are
congruent.