Dynamic Exploration of the Orthocenter of a Triangle

This interactive GeoGebra example dynamically demonstrates the geometric properties and locus of the orthocenter of a triangle as the vertices are dragged. The core mathematical concepts include triangle altitudes, the orthocenter, circumcenter, perpendicular bisectors, and polygon geometry. In terms of construction, it uses the Polygon command to define the base triangle, OrthogonalLine to construct altitudes, and combines commands like LineBisector, Intersect, Circle, Segment, and Angle to precisely build the circumcenter, the orthocenter, auxiliary segments, and angles. This tool is highly suitable for high school and middle school geometry courses, inquiry-based learning activities, and classroom teaching of triangle centers.