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Dividing a Line Segment into n Equal Parts
Click here for a printable line dividing worksheet
This page shows how to divide a line segment into n equal parts using only a compass and straightedge. We start with a given line segment AB, and end up with that segment divided into n equal segments. In the figure below, the construction is shown with n=5. It will work for any number however with the obvious changes.

Bear in mind if n is an integer power of 2, (2,4,8 etc) then another method is to use repeated bisection.

Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)

Step-by-step Instructions
These instructions correspond to the figure above and divide the line into 5 parts. Substitute the desired number in the appropriate places.
Step 1 From point A, draw a line segment at an angle to the given line, and about the same length. The exact length is not important.
Step 2 Set the compass on A, and set its width to a bit less than one fifth of the length of the new line.
Step 3 Step the compass along the line, marking off 5 arcs. Label the last one C.
Step 4 With the compass width set to CB, draw an arc from A just below it.
Step 5 With the compass width set to AC, draw an arc from B crossing the one drawn in step 4. This intersection is point D.
Step 6 Draw a line from D to B.
Step 7 Using the same compass width as used to step along AC, step the compass from D along DB making 4 new arcs across the line
Step 8 Draw lines between the corresponding points along AC and DB.
Step 9 Done. The lines divide the given line segment AB in to 5 congruent parts.
Try it yourself
Click here for a printable worksheet containing two line division exercises. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions

(C) 2008 Copyright John Page