Triangle Orthocenter Construction and Properties

This GeoGebra example dynamically demonstrates the orthocenter of a triangle—the common intersection point of its three altitudes. It illustrates the fundamental geometric fact that the three altitudes of any triangle are concurrent. Core concepts include the definition of the orthocenter, properties of altitudes, and intersections of lines and circles. The construction uses the Polygon command to create triangle ABC, Point for vertices, Line for drawing altitudes, and Intersect to find the foot of each altitude on the opposite side and the orthocenter H itself. A Circle is also used as an auxiliary element, with text objects labeling key points. This resource is ideal for middle or high school geometry classes, helping students visualize why the orthocenter exists and how its position changes for acute, right, and obtuse triangles.