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Math Help - is there converse for side splitter theorem?

  1. #1
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    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
    Last edited by mido22; September 18th 2012 at 04:00 PM.
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  2. #2
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    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.
    Thanks from mido22
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  3. #3
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    Re: is there converse for side splitter theorem?

    but i have only 2 proportional sides AB:BD=AC:CE=1:4 only
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  4. #4
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    Re: is there converse for side splitter theorem?

    Quote Originally Posted by mido22 View Post
    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.
    Thanks from mido22
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  5. #5
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    Re: is there converse for side splitter theorem?

    thNX very much
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