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Math Help - Help with a proof

  1. #1
    Newbie
    Joined
    Oct 2008
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    Help with a proof

    Could I please get some help with the following?
    Given a quadrilateral with points labeled sequentially A B C D with a line segment AC and a line sement BD in the interior noted at intersection by point E with the following givens: segment BC = segment CD and segment AB = segment AD


    Prove that AC is perpendicular to BD I'm stuck!
    thanks SO much for any help or hints
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, murphmath!

    Given a quadrilateral ABCD with diagonals AC and BD intersecting at point E,
    with the following givens: BC = CD and AB = AD.

    Prove that AC is perpendicular to BD.
    We have a kite-shaped figure . . .
    Code:
                A
                *
              * | *
            *   |   *
        D * - - + - - * B
           *    |E   *
            *   |   *
             *  |  *
              * | *
               *|*
                *
                C

    We are given: .  AB = AD,\;BC = CD

    Point A is equidistant from B and D.
    Point C is equidistant from B and D.

    Hence, AC is the perpendicular bisector of BD.

    . . Therefore: . AC \perp BD

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