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Quadrilaterals using Geometer's Sketchpad (Thumbnail Included)

  1. Feb 17, 2012 #1
    Hi Guys! I've attached a picture of the setup if you don't have Geometer's Sketchpad software. I honestly have no idea where to begin with this problem, as I've been staring at it for hours. Nevertheless, I've still put some thoughts down on what I think I should do.

    1. The problem statement, all variables and given/known data

    Use Geometer’s Sketchpad and draw points A, B, C (not all three are collinear).
    Construct segments AC and BC.
    Draw circle with center A and radius AC
    Draw circle with Center B and radius BC
    Label the other intersection of the circles D.
    Draw segments BD and AD.

    a. Drag point A, B, C, or D to change the shape of ABCD. What types of quadrilaterals can be formed? Explain.


    b. Are there types of quadrilaterals that cannot be formed? List and explain.


    3. The attempt at a solution

    Square – Yes. If the two circles have radii of the same length, and if you adjust points C and D accordingly, you can have all 90° angles.

    Rectangle – You can have a rectangle with all equal sides, but you can’t have a rectangle that isn’t a square, as the adjacent sides are always radii of the same circle, and cannot be different lengths.

    Rhombus – You can have a rhombus because you can have a square, and you could just adjust the angles if you wanted a rhombus that wasn’t a square?

    Parallelogram – You can have a parallelogram, but it has to be a rhombus as well, because adjacent sides must be equal.

    Kite – You can certainly have a kite, as the pairs of adjacent sides (radii) will always be equal.

    Any hints would be truly appreciated; I feel like an idiot staring at this problem in Geometer's Sketchpad.
     

    Attached Files:

  2. jcsd
  3. Feb 17, 2012 #2
    All quadrilaterals formed must be symmetric about AB.
    You can't create quadrilaterals that have 3 unequal sides or its sides crossed.
     
  4. Feb 17, 2012 #3
    Thanks for the response!

    So out of the list I've given, there are any of those that specifically can't be formed?
    Does this also imply that a trapezoid must be an isosceles trapezoid?
     
  5. Feb 17, 2012 #4
    The only trapezium can be formed is a square.
     
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