How to Bisect a Line With a Compass and Straightedge

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Bisecting a line (dividing a line in half) is easy enough if you know the length of the line, or can measure the line. But if you don’t know the length of the line, you can still bisect it using a straightedge and compass.

Part 1
Part 1 of 2:

Preparing the Compass

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    If the line segment is not already given, you will need to make it using a straightedge.
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    If you open the compass completely, and it spans one-half the length of the line or less, you need to choose a bigger compass. [1]
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    To do this, place the needle of the compass on either endpoint. Open the compass so that it spans a little more than half the length of the line. [2]
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Part 2
Part 2 of 2:

Bisecting the Line

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    Make sure the needle stays on the endpoint, and that you do not adjust the compass setting. [3]
    • The length of the arcs does not matter.
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    Make sure you do not change the compass setting. [4]
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    Make sure the needle stays on the endpoint, and that you do not adjust the compass setting. [5]
    • The two sets of arcs you’ve drawn should intersect.
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    To do this, place your straightedge on the point where the arcs above the line intersect, and align it with the point where the arcs below the line intersect. [6]
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    The line you draw between the two arc intersections bisects the line at a ninety degree angle. [7]
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    You have used the compass to outline two congruent circles centered over either endpoint. The intersecting arcs represent the endpoint of a radii from the center of either circle. [8]
    • The length of the radii will be the same, since the circles are the same size.
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  • Question
    How can I construct a line which bisects a given arc of a circle without center?
    Donagan
    Top Answerer
    Place the compass point at one end of the arc. Strike arcs of a given radius on each side of the circle's arc. Place the compass point at the other end of the circle's arc, and strike arcs of the same given radius on each side of the circle's arc so that they intersect the first two arcs you drew. Use the straightedge to draw a line connecting the two points where your arcs intersect each other. That line will bisect the circle's arc.
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    Not Helpful 9 Helpful 5
  • Question
    How do I construct a line that bisects a given arc of a circle?
    Donagan
    Top Answerer
    Treat the arc as if it were a straight line segment, and perform the operation shown in the article above. You can also strike arcs only on the outside of the circle and draw a line from their intersection to the center of the circle. That line will bisect the circle's arc.
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    Not Helpful 4 Helpful 5
  • Question
    How do I bisect a line segment into 1/2, 1/4 and so on?
    Donagan
    Top Answerer
    Perform the operation shown in the article above to bisect the line segment. Then do it again using only one-half of the line segment. Then do it again using only one-quarter of the line segment, etc.
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      Tips

      • If the two arcs do not intersect, then either you didn't draw the arcs long enough, or you didn't open the compass wide enough. Erase the arcs, open the compass wider, and try again. [9]
        Thanks
      • Keep the pencil tip sharp. If it gets dull, the wide lines it makes can lead to errors when placing the compass point or the ruler.
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      Warnings

      • Make sure you do not change the compass width when you switch from one endpoint to the other. [10]
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      References

      1. ↑ https://www.mathsisfun.com/geometry/construct-linebisect.html
      2. ↑ http://www.mathopenref.com/constbisectline.html
      3. ↑ https://www.mathsisfun.com/geometry/construct-linebisect.html
      4. ↑ https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-bisectors/v/constructing-a-perpendicular-bisector-using-a-compass-and-straightedge
      5. ↑ https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-bisectors/v/constructing-a-perpendicular-bisector-using-a-compass-and-straightedge
      6. ↑ https://www.ck12.org/geometry/construct-bisectors-of-line-segments-and-angles/lesson/Bisectors-of-Line-Segments-and-Angles-GEOM-HNRS/
      7. ↑ https://www.ck12.org/geometry/construct-bisectors-of-line-segments-and-angles/lesson/Bisectors-of-Line-Segments-and-Angles-GEOM-HNRS/
      8. ↑ https://www.ck12.org/geometry/construct-bisectors-of-line-segments-and-angles/lesson/Bisectors-of-Line-Segments-and-Angles-GEOM-HNRS/
      9. ↑ https://mathbitsnotebook.com/Geometry/Constructions/CCconstruction2.html
      1. ↑ https://mathbitsnotebook.com/Geometry/Constructions/CCconstruction2.html

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