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Dividing a line segment into equal parts

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

  After doing this Your work should look like this
  Start with a line segment AB that we will divide up into 5 (in this case) equal parts. Geometry construction with compass and straightedge or ruler or ruler
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. Geometry construction with compass and straightedge or ruler or ruler
Step 2 Set the compasses on A, and set its width to a bit less than one fifth of the length of the new line. Geometry construction with compass and straightedge or ruler or ruler
Step 3 Step the compasses along the line, marking off 5 arcs. Label the last one C. Geometry construction with compass and straightedge or ruler or ruler
Step 4 With the compasses' width set to CB, draw an arc from A just below it. Geometry construction with compass and straightedge or ruler or ruler
Step 5 With the compasses' width set to AC, draw an arc from B crossing the one drawn in step 4. This intersection is point D. Geometry construction with compass and straightedge or ruler or ruler
Step 6 Draw a line from D to B. Geometry construction with compass and straightedge or ruler or ruler
Step 7 Using the same compasses' width as used to step along AC, step the compasses from D along DB making 4 new arcs across the line Geometry construction with compass and straightedge or ruler or ruler
Step 8 Draw lines between the corresponding points along AC and DB. Geometry construction with compass and straightedge or ruler or ruler
Step 9 Done. The lines divide the given line segment AB in to 5 congruent parts. Geometry construction with compass and straightedge or ruler or ruler

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Right triangles

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Polygons

Non-Euclidean constructions