### Construction of a Regular Hexagon

```GeoGebra 4.0: Regular Hexagon Construction Activity: Regular Hexagon Construction Objectives 1. Becoming familiar with the basic use of tools and formatting 2. To understand the properties of a Hexagon and how this translates to a construction in GeoGebra. •
Introduction: In this activity you are going to use the following tools. Make sure you know how to use each tool before you begin with the actual construction of the hexagon: Circle with center through point Intersect two objects Angle Show / hide object Polygon Move Hint: Look at the file Regular_Hexagon_Construction.ggb, if you are not sure about the construction process. Preparing the Window: • Open a new GeoGebra file. • Hide the algebra window, the axes on and the input field. Set labeling to New Points Only. Construction process: 1. Use the Circle with center through point tool to draw a circle a with center A through point B 2. Use the Circle with center through point tool to construct circle b with center B through point A 3. Use the intersect two objects tool to mark the Intersections between the two circles in order to create points C and D. 4. Use the Circle with center through point tool to construct circle c with center C through point A. 5. Use the intersect two objects tool to mark the new Intersection between the circle c and circle a in order to create point E. 6. Use the Circle with center through point tool to construct circle d with center D through point A. 7. Use the intersect two objects tool to mark the new Intersection between the circle d and circle a in order to create point F. 8. Use the Circle with center through point tool to construct circle e with center E through point A. 9. Use the intersect two objects tool to mark the new Intersection between the circle e and circle a in order to create point G. 10. Use the polygon tool to create hexagon FGECBD. 11. Use the angle tool and click the hexagon to create the interior angles. Hint: Go to Edit Object Properties choose the angles and uncheck Allow reflex. GeoGebra 4.0: Regular Hexagon Construction The following Image is what your file should look like before hiding any objects or formatting the hexagon. Formatting: Select Edit Object properties and format your object in anyway you wish and save your file. Challenge Questions: 1) Could we have used less circles in our construction process? 2) Can you to come up with an explanation for this construction process. Hint: Which radius do the circles have and why? ```