Regular Hexagon Construction
Explore the geometric properties of a regular hexagon
Summarize the properties of a regular hexagon before you start your actual construction.
Hint: If you are not familiar with the construction steps necessary for a regular hexagon construction, you might want to explore the applet below. Just use the buttons of the Navigation Bar in order to replay the construction steps.
Task
Construct a regular hexagon that passes the drag test by following the construction steps provided below.
Try it yourself...
Construction steps
| 1. |  | Draw a circle c with center A through point B. | 7. |  | Intersect the new circle f with circle c in order to get vertex F. | |
| 2. | | Construct a new circle d with center B through point A. | 8. | | Construct a new circle g with center E through point A. | |
| 3. | | Intersect the circles c and d to get the hexagon’s vertices C and D. | 9. | | Intersect the new circle g with circle c in order to get vertex G. | |
| | | Hint: Selecting circle d and circle c creates both intersection points. | 10. |  | Draw a hexagon in counter-clockwise orientation using the intersection points of the circles. | |
| 4. | | Construct a new circle e with center C through point A. | 11. |  | Hide the circles. | |
| 5. | | Intersect the new circle e with circle c in order to get vertex E. | 12. |  | Display the interior angles of the hexagon. | |
| | | Hint: If you just want a single intersection point, click directly on the intersection of the two circles. | | Hint: If you get the exterior angles, you probably created the hexagon in clockwise orientation. | ||
| 6. | | Construct a new circle f with center D through point A. | 13. |  | Perform the drag test to check if your construction is correct. |
Back to school...
Try to find an explanation for this construction process.
Hint: Which radius do the circles have and why?