How to Bisect a Line With a Compass and Straightedge

Two Parts:Preparing the CompassBisecting the Line

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
Preparing the Compass

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    Draw the line segment you need to bisect. If the line segment is not already given, you will need to make it using a straightedge.
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    Choose an appropriately sized compass. 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.
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    Position the compass on an endpoint. 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.[1]

Part 2
Bisecting the Line

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    Draw an arc above and below the line segment. Make sure the needle stays on the endpoint, and that you do not adjust the compass setting.
    • The length of the arcs does not matter.
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    Reposition the compass on the other endpoint. Make sure you do not change the compass setting.
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    Draw another set of arcs, above and below the line segment. Make sure the needle stays on the endpoint, and that you do not adjust the compass setting.
    • The two sets of arcs you’ve drawn should intersect.
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    Connect the arc intersections. 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.
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    Draw your perpendicular bisector. The line you draw between the two arc intersections bisects the line at a ninety degree angle.
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    Understand why this works. 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.
    • The length of the radii will be the same, since the circles are the same size.[2]

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.
  • 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.

Warnings

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

Article Info

Categories: Compass Constructions