Thread: is there converse for side splitter theorem?

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

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.

but i have only 2 proportional sides AB:BD=AC:CE=1:4 only

Originally Posted by mido22

but i have only 2 proportional sides AB:BD=AC:CE=1:4 only

Use condition #3 (two sides in the same ratio with the same angle between them) here.

thNX very much