Yes, and it is easy to prove. Because of the proportions, the triangles ABC and ADE are "similar" so have congruent angles. The by "corresponding angles" the lines are parallel.
I know that :-
if a line is parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally.
but
if i have that the line divides the two sides proportionally can i get that this line is parallel to the 3rd side
if i have AB:BD=AC:CE=1:4
is it true to say that BC // DE