Orthocenter Construction and Properties in a Triangle

①This GeoGebra example dynamically demonstrates the geometric fact that the three altitudes of any triangle intersect at a single point, the orthocenter, and shows its relationship with vertices, sides, and angles. ②Core mathematical concepts include the definition of the orthocenter, perpendicularity of altitudes, and how the orthocenter's position changes for acute, right, and obtuse triangles (inside, at a vertex, or outside). ③Construction details: use the Polygon command to create triangle ABC, the OrthogonalLine command to draw perpendiculars from each vertex to the opposite side, the Intersect command to find the feet and the orthocenter, the Segment command to draw the altitudes, and the Angle command to label relevant angles, resulting in a complete orthocenter construction. ④This is suitable for middle/high school geometry lessons, math competition training, or dynamic geometry exploration, helping students intuitively grasp the properties of the orthocenter, one of the triangle's five centers, and its dependence on triangle shape.