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Math Help - congruence of two triangles

  1. #1
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    congruence of two triangles

    Problem: In ΔABC, D is on segment BC, E is on AC and F is the intersection of segments EB and AD. Assume further that ACBC and ECDC. Prove ΔAFE ≅ ΔBFD.
    The picture is given as an attachment.

    Show
    △AFE△BFD
    * Oh anything such as
    AC≅BC are line segments without the line notation on top of each pair of points. I couldn't figure it out with latex.

    Partially completed proof
    1. A
    ssume AC≅BC amd EC≅DC. 1. Assumption
    D is on segment BC, E is on AC
    F is the intersection of segments
    EB and AD

    2.
    AFB DFB 2. Vertical angles
    //EFD AFB

    3.
    AE is congruent to DB 3. derived from step 1

    4.
    CAB CBA 4. Lemma A- In △ABC if AC≅BC then the base angles are congruent

    5.
    △ABC is an isosceles 5. Isosceles triangle theorem- A triangle is isosceles iff the base angles are congruent.
    triangle

    6.
    AB≅AB 6. Reflexive property

    7.
    △ADB△AEB. 7. SAS postulate

    8.

    I almost have everything but I just can't seem to figure these last steps. Somehow I don't know how to show point F where the two line segments EB and AD meet is the midpoint or something.




    I got it. I concluded with ASA.
    Attached Thumbnails Attached Thumbnails congruence of two triangles-triangle.jpg  
    Last edited by bonfire09; February 1st 2013 at 12:45 PM.
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  2. #2
    MHF Contributor

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    Re: congruence of two triangles

    You have not completely stated the problem, just given a picture. What are you given about the lengths and angles here? You start with "1. Assume AC≅BC amd EC≅DC. 1. Assumption" Are you given that? Is that said in some part of the problem you haven't shown? If not, how can you simply "assume" it? If you are given it, then you should have said that here.
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  3. #3
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    Re: congruence of two triangles

    Oh ok Ive fixed that part. I put the entire question up.
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