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Math Help - midpoints of triangles

  1. #1
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    Question midpoints of triangles

    so the problem says use triangle ghj, where a,b,c are the midpoints. if ab= 3x +8 and gj= 2x + 24, what is ab? i have no idea what that says it's like talking latin. help!!!!!!!!!!!
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  2. #2
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    Quote Originally Posted by Pai-Pai View Post
    so the problem says use triangle ghj, where a,b,c are the midpoints. if ab= 3x +8 and gj= 2x + 24, what is ab? i have no idea what that says it's like talking latin. help!!!!!!!!!!!
    You have to use the "mid parallel theorem" (I don't know if this is the appropriate expression in English): "The connection of the midpoints of two sides of a triangle is parallel to the third side and has half of the length of the third side"

    I've attached a sketch.

    From your question you know that

    2 \cdot |\overline{AB}| = |\overline{GJ}|

    2(3x+8) = 2x+24 ~\implies~x = 2

    Therefore |\overline{AB}| = 14
    Attached Thumbnails Attached Thumbnails midpoints of triangles-dreieck_mittenparallele.png  
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