Orthocenter Construction and Dynamic Exploration

This GeoGebra example demonstrates the classic geometric phenomenon that the three altitudes of a triangle are concurrent at a single point, known as the orthocenter. The core mathematical concepts involved include the orthocenter, centroid or barycenter, linear functions, and basic properties of triangles. The construction uses GeoGebra commands such as Segment and OrthogonalLine to draw altitudes from each vertex to the opposite side, creating objects like D, E, f, g, h, i, j, and k, and then identifies their intersection as the orthocenter. This example is suitable for middle and high school geometry classes, helping students visually grasp the existence and uniqueness of the orthocenter, and explore how its position changes for acute, right, and obtuse triangles. It serves as an excellent resource for geometric construction practice and dynamic investigation.