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Math Help - Constructing an angle using only a ruler and compasses...?!?!

  1. #1
    Junior Member Turple's Avatar
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    Question Constructing an angle using only a ruler and compasses...?!?!

    Hi I needed to construct a 60 degree angle with only a ruler and compasses. I understand how to construct an angle of 90 degrees, and how to do an angle bisector but cannot understand how to do this.

    Thankyou
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by Turple View Post
    Hi I needed to construct a 60 degree angle with only a ruler and compasses. I understand how to construct an angle of 90 degrees, and how to do an angle bisector but cannot understand how to do this.

    Thankyou
    In an equilateral triangle, angles are 60 degrees.

    So you can try to do this way :

    - let A and B be two points of the plane
    - get the length AB with your compass
    - draw the circle of center A, and length AB. This will make all the points that are at equal distance to A than B.
    - draw the same circle, but of center B. This will make all the points that are at equal distance to B than A.

    There will be two intersections. See what the properties of the sides of the formed triangle are
    Last edited by Moo; May 16th 2008 at 09:26 AM. Reason: "interesections", whazzat ? :D
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    Hello, Turple!

    I needed to construct a 60 angle with only a ruler and compass.
    We need to construct an equilateral triangle.

    Draw a horizontal line; label the left end A.

    Open your compass to a convenient spread (and don't change it).
    Place the point on A and swing an arc cutting the line at B.

    Keep the point on A and swing an arc above the line.
    Place the point on B and swing an arc cutting the first arc at C.

    Triangle ABC is equilateral.

    Therefore: . \angle A \,=\,\angle B\,=\,\angle C \,=\,60^o


    Edit: Too fast for me, Moo!
    .
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  4. #4
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    Quote Originally Posted by Turple View Post
    Hi I needed to construct a 60 degree angle with only a ruler and compasses. I understand how to construct an angle of 90 degrees, and how to do an angle bisector but cannot understand how to do this.

    Thankyou
    Here comes the result:
    Attached Thumbnails Attached Thumbnails Constructing an angle using only a ruler and compasses...?!?!-sechziggrad.gif  
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  5. #5
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    Quote Originally Posted by Turple View Post
    Hi I needed to construct a 60 degree angle with only a ruler and compasses. I understand how to construct an angle of 90 degrees, and how to do an angle bisector but cannot understand how to do this.

    Thankyou
    1. Draw a circle around midpoint M
    2. Draw a diameter. I labeled the endpoints of the diameter by A and B.
    3. Construct a perpendicular bisector of MB which cuts the circle line in 2 points.
    4. Connect one of the intersection points with M. I've labeled the point in question by C.
    5. The angle \angle(BMC)=60^\circ

    By the way: This method is very convenient to construct a regular hexagon. I've marked the vertices of the hexagon in red.
    Attached Thumbnails Attached Thumbnails Constructing an angle using only a ruler and compasses...?!?!-sechziggrd2.gif  
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