GeoGebra 4.0: Triangle Incenter Construction Activity: Triangle Incenter Construction • Objectives 1. Becoming familiar with the basic use of tools and formatting 2. To understand the properties of a triangle and how they can be used to construct an Incenter. Introduction: In this activity you are going to use the following tools. Please, make sure you know how to use each tool before you begin with the actual construction of the incenter: Polygon Intersect two objects Angular Bisector Perpendicular Line Circle with center through point Move Show / hide label Hint: If you are not sure about the construction process, you might want to have a look at the file, Incenter.ggb. 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 Polygon tool to create an arbitrary triangle ABC. 2. Use the Angle Bisector tool to construct the angle bisector for each vertex of the triangle. Hint: The tool, Angle Bisector, can used by selecting the three points that make up the angle. 3. Use the Intersect Two Objects tool to mark the intersection point D of two of the line bisectors. Hint: The tool, Intersect Two Objects, can’t be applied to the intersection of three lines. 4. Use the Perpendicular Line tool and select point D and any of the sides of triangle ABC. 5. Use the Intersect Two Objects tool to mark the intersection point E of two of the line from step 4 and the side of the triangle. 6. Use the Circle with Center Through Point tool and select Point D and then Point E. 7. Perform the drag test to check if your construction is correct. GeoGebra 4.0: Triangle Incenter Construction The following Image is what your file should look like before hiding or formatting any objects. Challenge: Modify your construction to answer the following questions: 1. Can the Incenter of a triangle lie outside the triangle? If yes, for which types of triangles is this true? 2. Try to find an explanation for using angle bisectors in order to create the Incircle of a triangle.