Dynamic Construction and Properties of the Orthocenter of a Triangle (1)

①This GeoGebra example dynamically constructs the three altitudes of an arbitrary triangle and visually demonstrates that they concur at a single point, the orthocenter. ②Core mathematical concepts include the orthocenter, altitudes, perpendicularity, intersection points, and how the orthocenter's position relates to the triangle's angles (inside for acute triangles, outside for obtuse, at a vertex for right triangles). ③Construction details: The Polygon command creates triangle ABC; OrthogonalLine draws perpendiculars from each vertex to the opposite side; Intersect finds the altitude intersections; Segment and Angle mark the altitudes and angles; text1 labels the orthocenter. ④Suitable for middle school to high school geometry lessons on the five centers of a triangle (centroid, circumcenter, incenter, orthocenter, excenter), ideal for teacher demonstrations or student exploration by dragging vertices to observe how the orthocenter moves.