Introduction to Constructions

David Wees, 12.12.2018

This is a sequence of geometric constructions, each designed as puzzles, where what students figure out how to do in one step can be used in future constructions. I recommend students using Geogebra first and then transferring their constructions (once they have them figured out) to paper using a compass and straightedge.


  • 1. #1 Draw a Circle
  • 2. #2 Given a Line Segment, Draw Another
  • 3. #3 Given a Line Segment, Draw Another
  • 4. #4 Double the length of a line segment
  • 5. #5 Triple a Line Segment
  • 6. #6 Draw Two Circles
  • 7. #7 Draw an Equilateral Triangle
  • 8. #8 Draw Three Circles
  • 9. #9 Two Circles That Touch Once
  • 10. #10 Draw Three Overlapping Circles
  • 11. #11 Draw a regular hexagon
  • 12. #12 Optimal Regular Hexagon
  • 13. #13 Construct Perpendicular Lines
  • 14. #14 Find the Midpoint
  • 15. #15 Construct 2 Circles Inside a 3rd
  • 16. #16 Construct a square
  • 17. #17 Construct an Octagon

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#1 Draw a Circle

Given a line segment, draw a circle with its radius as the line segment.
– David Wees

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