Geometric construction of a hexagon

Question

How to draw a hexagon with each of its interior angles as 120° using a ruler and a compass? Please help me out.. actually the 6th side I am drawing is becoming slanting in place of being parallel to the first side

Answer 1

A low-error method:

• Mark a point for the centre of the hexagon.
• Draw a circle that will contain the hexagon - keep the compasses fixed.
• Draw a diameter through the circle - this intersects the circle at two points of the hexagon.
• At each of these points, draw an arc the same radius as the circle to find the other four points of the hexagon
• Join the intersection points on the containing circle for your regular hexagon.

Answer 2

This is the one where you keep your compass at the same setting you used to draw the circle, and use it to step off six equal arcs, right? Probably what is happening is that you accumulate errors as you go round the circle and the problem is how to prevent this. Begin by drawing a diameter to your circle and start your arcs at one end of it. You know that three steps should take you to the opposite end. If you can see that a small error has crept in, it will be easier to correct at this stage.

COMMMENT I see that Joffan and myself posted simultaneously. Their solution is better!

Answer 3

Draw a circle, draw a diameter of the circle. Let's say diameter intersects circle in points A and B. Draw two more circles with the same radius and using A and B as centers. The intersection points with the first circle will be your vertices (plus A and B). You need to be really accurate.