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Math Help - Help with simple internal line segments of triangles proof.

  1. #1
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    Help with simple internal line segments of triangles proof.

    Prove that if D is internal to \overline{AB}, E is internal to \overline{AC} and \frac{DB}{ DA} = \frac{EC}{EA} then {BC} is parallel to {DE}



    I'm having a tough time figuring out where to start or how to go about doing this proof, we've been focusing on Ceva's theorem as of late so I'm thinking I have to incorporate it some how.
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  2. #2
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    Quote Originally Posted by jpatrie View Post
    Prove that if D is internal to \overline{AB}, E is internal to \overline{AC} and \frac{DB}{ DA} = \frac{EC}{EA} then {BC} is parallel to {DE}



    I'm having a tough time figuring out where to start or how to go about doing this proof, we've been focusing on Ceva's theorem as of late so I'm thinking I have to incorporate it some how.
    First re-write the given equality:

    \frac{DB}{ DA} = \frac{EC}{EA}

    \frac{DB+DA}{ DA} = \frac{EC+EA}{EA}

    \frac{AB}{AD} = \frac{AC}{AE}

    \frac{AD}{AB} = \frac{AE}{AC}

    Then look at the triangles ABC and ADE. What can you say about them?
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