Question

converse of thales theorem

Answer 1

take a triangle ABC .given
construction draw a line DF

proof; to prove that DE//BC
   let us take DE is not parllel to BC and DF//BC

by thales therom AD/DB=AF/FC
from this we get F=E
But ED IS NOT PARALLEL to BC 
therefore DE//BC

Answer 2

Answer:

If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.