These constructions use a compass and straight edge only.
A perpendicular line is at 90° to another line.
Given a horizontal line and a point A
- With point of compasses on A construct two arcs at B and C
- Open compasses wider. With point on B draw two arcs at E and F
- Keeping width of compasses the same, place p[oint on C and draw two arcs also at E and F
- Use straight edge to connect intersection of arcs at E and F
- Place point of compasses on B and construct arcs at E and F
- Place point of compasses in turn on E and F and construct arcs at G
- Use straight edge to connect B and G
- 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)
- Keeping width of the compasses unaltered, place point on D and mark off an arc at C.
- 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.