Orthocenter of a Triangle: Construction and Properties

①This GeoGebra example dynamically demonstrates the geometric fact that the three altitudes of a triangle intersect at a single point, the orthocenter, and shows how its position changes for acute, right, and obtuse triangles. ②The core mathematical concept is the orthocenter of a triangle, defined as the common intersection of the three altitudes, involving perpendicularity, collinearity, and concurrency. ③Construction details: using commands such as Circle, Point, Polygon, Intersect, Segment, and Angle, the example builds a triangle, draws its altitudes by intersecting perpendiculars with opposite sides, marks right angles, and identifies the orthocenter via intersection or a dedicated tool, with a text label. ④This is suitable for middle or high school geometry classes to explore the definition, existence, and dynamic behavior of the orthocenter, and to investigate how it relates to triangle types, serving as an interactive tool for geometric discovery and construction practice.