is there converse for side splitter theorem?[SOLVED]

**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

http://www.mathwarehouse.com/geometr...er-theorem.gif

if i have AB:BD=AC:CE=1:4

is it true to say that BC // DE

Re: is there converse for side splitter theorem?

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.

Re: is there converse for side splitter theorem?

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

Re: is there converse for side splitter theorem?

Quote:

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.

Re: is there converse for side splitter theorem?