How to Bisect a Line With a Compass and Straightedge

PDF download Download Article
PDF download Download Article

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

PDF download Download Article
  1. If the line segment is not already given, you will need to make it using a straightedge.
  2. 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]
    Advertisement
  3. 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]
    4. Advertisement
Part 2
Part 2 of 2:

Bisecting the Line

PDF download Download Article
  1. 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.
  2. Make sure you do not change the compass setting. [4]
  3. 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.
  4. 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]
  5. The line you draw between the two arc intersections bisects the line at a ninety degree angle. [7]
  6. 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.
    7. Advertisement

Community Q&A

Search
Add New Question
  • 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.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 10 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.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    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.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 5 Helpful 8
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Video

      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
        Helpful 1 Not Helpful 1
      • 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.
        Thanks
        Helpful 5 Not Helpful 3
      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Name
      Please provide your name and last initial
      Submit
      Thanks for submitting a tip for review!
      Advertisement

      Warnings

      • Make sure you do not change the compass width when you switch from one endpoint to the other. [10]
        Thanks
        Helpful 3 Not Helpful 0
      Advertisement

      You Might Also Like

      How to
      Find the Perpendicular Bisector of Two Points
      How to
      Calculate the Area of Any Quadrilateral: A Step-by-Step Guide
      How to
      Draw a Hexagon
      How to
      Construct a Regular Pentagon
      How to
      Construct a 60 Degrees Angle Using Compass and Ruler
      How to
      Construct a Line Parallel to a Given Line Through a Given Point
      How to
      Construct a 30 Degrees Angle Using Compass and Straightedge
      How to
      Construct a 90 Degrees Angle Using Compass and Ruler
      How to
      Create a Regular Heptagon
      How to
      Construct a Perpendicular Line to a Given Line Through Point on the Line
      Advertisement

      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

      About This Article

      In other languages
      Thanks to all authors for creating a page that has been read 130,124 times.

      Reader Success Stories

      • Buthesh Perera

        Jul 31, 2016

        "Really helps. I always use wikiHow for problems. Thanks!"
      Share your story

      Did this article help you?

      Advertisement