Dynamic Construction of the Orthocenter of a Triangle

This GeoGebra example dynamically demonstrates the construction of the orthocenter of a triangle. The core mathematical concept is the orthocenter, the intersection point of the three altitudes of a triangle, one of the five classical triangle centers with significant geometric properties. The construction steps include: creating triangle poly1 with vertices A, B, C using the Polygon command; drawing perpendicular lines from each vertex to the opposite side using the OrthogonalLine command (resulting in lines c, a, b, d, e, f); and finding their intersection point D using the Intersect command, which is the orthocenter, with a text label text1. This example is suitable for middle and high school geometry classes, helping students visually grasp the definition of the orthocenter, the concurrency of altitudes, and how its position varies among acute, right, and obtuse triangles.