Thread: is there converse for side splitter theorem?

1. 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

if i have AB:BD=AC:CE=1:4
is it true to say that BC // DE

2. 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.

3. Re: is there converse for side splitter theorem?

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

4. Re: is there converse for side splitter theorem?

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.

5. Re: is there converse for side splitter theorem?

thNX very much

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