Geometrical Considerations


These constructions use a compass and straight edge only.

A perpendicular line is at 90° to another line.

Perpendicular Line to a Given Point on a Line

Given a horizontal line and a point A

  1. With point of compasses on A construct two arcs at B and C
  2. Open compasses wider. With point on B draw two arcs at E and F
  3. Keeping width of compasses the same, place p[oint on C and draw two arcs also at E and F
  4. Use straight edge to connect intersection of arcs at E and F

Bisecting an Angle

  1. Place point of compasses on B and construct arcs at E and F
  2. Place point of compasses in turn on E and F and construct arcs at G
  3. Use straight edge to connect B and G

Constructing 60° Angle (or Equilateral Triangle)

  1. With point of compasses at A, construct arc at D and C (or else draw complete single arc as in figure, if you are unsure of the general area where the final line will be drawn)
  2. Keeping width of the compasses unaltered, place point on D and mark off an arc at C.
  3. Use straight edge to connect A to C.

Hopefully you can see how this works. By connecting D to C with a straight edge, you will have an equilateral triangle.