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Math Help - Triangle Construction

  1. #1
    Junior Member
    Joined
    Apr 2008
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    30

    Triangle Construction

    Does anyone have an algorithm for constructing a triangle given one side, AB, and altitudes h and k from A and B respectively? (Using straightedge compass construction)
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  2. #2
    Super Member

    Joined
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    From
    Lexington, MA (USA)
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    Hello, GoldendoodleMom!

    Find an algorithm for constructing a triangle given one side, AB,
    and altitudes h and k from A and B respectively.
    (Using straightedge-compass construction)

    Draw line segment AB.
    Locate its midpoint M.
    Draw a semicircle with diameter AB.
    Code:
                  * * *
              *           *
            *               *
           *                 *
    
          *                   *
        A * - - - - * - - - - * B
                    M

    With A as center and radius h, swing an arc cutting the semicircle at P.

    With B as center and radius k, swing an arc cutting the semicircle at Q.

    Code:
                  Q
                  ∆ * *     P
              *     ∆     o
            *         ∆     *
           *       o    ∆    *
                o         ∆
          *  o              ∆ *
        A o - - - - * - - - - ∆ B
                    M

    Draw  AQ and BP, extending them to meet at C.

    The required triangle is \Delta ABC.

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  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    1

    Triangle Construction

    Hello
    For the past few days, I've been searching on the Internet for a triangle construction from its orthocenter, circumcenter and incenter. Unfortunately,I didn't find anything. Does anyone know something about this construction?
    Thank you.
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