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GeoGebraGeoGebra Classroom

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.Toolbar ImageDraw a circle c with center A through point B.7.Toolbar ImageIntersect the new circle f with circle c in order to get vertex F.
2.Toolbar ImageConstruct a new circle d with center B through point A.8.Toolbar ImageConstruct a new circle g with center E through point A.
3.Toolbar ImageIntersect the circles c and d to get the hexagon’s vertices C and D. 9.Toolbar ImageIntersect 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. Toolbar ImageDraw a hexagon in counter-clockwise orientation using the intersection points of the circles.
4.Toolbar ImageConstruct a new circle e with center C through point A.11. Toolbar ImageHide the circles.
5.Toolbar ImageIntersect the new circle e with circle c in order to get vertex E.12.Toolbar ImageDisplay 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.Toolbar ImageConstruct a new circle f with center D through point A.13.Toolbar ImagePerform the drag test to check if your construction is correct.
Hint: You might want to save your construction using the File menu.

Back to school...

Try to find an explanation for this construction process. Hint: Which radius do the circles have and why?