GeoGebra 4.0: Triangle Orthocenter Construction Activity: Triangle Orthocenter 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 a Orthocenter. Introduction: In this activity you are going to use the following tools. Familiarize yourself with
these tools before you begin with the actual construction of the orthocenter:
Polygon
Intersect two objects
Perpendicular Line
Move
Hint: If you are not sure about the construction process, you might want to have a look at the file, Orthocenter.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 Perpendicular Line tool to construct the Altitude for each side of the triangle. Hint: The Altitudes for a triangle are the lines drawn through a vertex and perpendicular to the opposite side of the triangle. 3. Use the Intersect two objects tool to mark the intersection Point D of two of the Altitudes. Hint: The tool, Intersect two objects, can’t be applied to the intersection of three lines. 4. Perform the drag test to check if your construction is correct. GeoGebra 4.0: Triangle Orthocenter 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 orthocenter of a triangle lie outside the triangle? If yes, for which types of triangles is this true?