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Simple geometric proof

  1. Apr 2, 2007 #1
    I have a simple geometric proof (first proofs) I can't finish. Looks like this:

    A________L


    C________E

    suppose there's a straight line from l to c and a to e (to make an x) and a midpoint I.

    It says: Given I is the midpoint of both [tex]\overline{AE}[/tex] and [tex]\overline{LC}[/tex]; AE = LC
    Prove AI = LI

    ??

    I'm not sure where to go except to start with the given. How do I complete (or start) the proof using the midpoint postulate and betweenness of lines theorm.
     
  2. jcsd
  3. Apr 2, 2007 #2

    arildno

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    Now, you DO know that I is the MIDPOINT of each line segment.

    Therefore, you know that:
    AI=IE and LI=IC

    Furthermore,

    you have the equations:
    AE=LC (given)
    AI+IE=AE (betweenness of points)
    LI+IC=LC (the same)

    Now, can you jumble about these 5 equations to get your result?
     
  4. Apr 6, 2007 #3
    AE = LC (given)
    AI+ IE = AE (betweeness of points)
    LI + IC = LC (the same)
    AI=IE
    LI=IC
    Therefore AI = LI because AE = LC so the segments would be equal.

    That's what i could come up with with those equestions.
     
  5. Apr 7, 2007 #4

    arildno

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    At this level, your logic should be a bit more thorough than that.
    Since IE=AI and IC=LI, we have:

    2AI=AE and 2LI=LC
    Thus, we get:
    2AI=2LI, implying AI=LI
     
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