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Math Help - I have Another Triangle Question!!!!!

  1. #1
    Newbie joesmith13610's Avatar
    Joined
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    Oregon
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    I have Another Triangle Question!!!!!

    Construct triangle given side a, Ha(height at side A), Ma(median of side a).


    for this problem is it possible that Ha = Ma? Cause this is where I am stuck.
    if Ha = Ma, then my problem is solved, because they both meet at the perpendicular bisector of side a, which is where the midpoint lie. Which means my median and height will also intersect. right??


    thanks for all your help.
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, Joe!

    The wording is rather clumsy . . .


    Construct a triangle given: side a,\;H_a (altitude to side a), M_a (median to side a).

    Draw a horizontal line L.

    Erect a perpendicular to line L and measure length H_a to point A.
    Code:
              A
              *
              |
              |
           Ha |
              |
              |
        L - - * - - - - - - - - - - - - - -

    Using center A and radius M_a, swing an arc cutting line L at D.
    Code:
              A
              *
              |\
              | \
           Ha |  \ Ma
              |   \
              |    \
        L - - * - - * - -
                    D

    D is the midpoint of side a.

    Using center D and radius \tfrac{1}{2}a, swing arcs on both sides
    . . cutting line L at B and C.
    Code:
              A 
              *
             *|\ *
            * | \   *
           *  |  \     *
          *   |   \       *
         *    |    \         *
        *  *  *  *  *  *  *  *  *
        B    Ża     D    Ża     C

    And ABC is our triangle!

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  3. #3
    Newbie joesmith13610's Avatar
    Joined
    Oct 2008
    From
    Oregon
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    so we first construct a line segment BD that is 1/2 of length side a, and find the perpendicular bisector? is that correct?
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