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Math Help - Parts of parallel lines are parallel is a postulate or theorem?

  1. #1
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    Parts of parallel lines are parallel is a postulate or theorem?

    I encountered a proof problem where I was given parallelogram ABCD and that AE is congruent to FC. I had to prove EBFD was a parallelogram. I want to use the theorem that if one pair of sides of a quadrilateral is both congruent and parallel, then it is a parallelogram. In doing so, I would like to say that EB is parallel to FD because parts of parallel lines are parallel. Is that a postulate?
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  2. #2
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    Hello lamp23,
    Yes its a postulate but what makes the other pair parallel

    bjh
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  3. #3
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    Quote Originally Posted by lamp23 View Post
    I encountered a proof problem where I was given parallelogram ABCD and that AE is congruent to FC. I had to prove EBFD was a parallelogram. I want to use the theorem that if one pair of sides of a quadrilateral is both congruent and parallel, then it is a parallelogram. In doing so, I would like to say that EB is parallel to FD because parts of parallel lines are parallel. Is that a postulate?
    If I were you I'd prove the parallelogram by using simple facts about triangles and angles.
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    Right, I understand that I can do it with angles but what was first apparent to me was using the theorem that if a quadrilateral has one pair of opposite sides that is both parallel and congruent then it is a parallelogram. Anyway, I wrote this:


    S: (line segment)AB || (line segment)DC R: Opposite sides of parallelograms are parallel.


    S: (line segment)EB || (line segment)DF R: Line segments contained within parallel lines are parallel.


    I wasn't sure if somewhere in the proof I should be including another statement that says (line)AB || (line)DC
    Last edited by lamp23; February 23rd 2011 at 10:42 AM.
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  5. #5
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    parallelogram

    Hi lamp23,

    Your diagram

    ABCD is a parallelogram
    AE is congruent FC
    Prove EBFD is a parallelogram

    Angle A = Angle C why
    AE = CF given
    AD = BC why
    Triangles DAE and BCF are congruent why

    continue and prove that DE is parallel toFB



    bjh
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  6. #6
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    Quote Originally Posted by bjhopper View Post
    Hi lamp23,

    Your diagram

    ABCD is a parallelogram
    AE is congruent FC
    Prove EBFD is a parallelogram

    Angle A = Angle C why
    AE = CF given
    AD = BC why
    Triangles DAE and BCF are congruent why

    continue and prove that DE is parallel toFB



    bjh
    It's not that I'm having trouble find a proof. I just wanted to know if the proof I chose was valid (which it would be as long as "Line segments contained within parallel lines are parallel." is a postulate).
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  7. #7
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    "Parts of parallel lines are parallel" is neither a postulate nor a theorem because we do not define "parallel segments". I think what you want to say is not that "part of the line" or "segments of the line" are parallel but that the two segments lie on parallel lines. Once you have said that you can use the fact that the lines, not the segments, are parallel.
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