Orthocenter of a Triangle: Dynamic Construction and Properties

①This GeoGebra example dynamically demonstrates the classic geometric fact that the three altitudes of a triangle intersect at a single point, the orthocenter. ②Core mathematical concepts include the orthocenter, altitudes, perpendicularity, and the positional relationships among the orthocenter, vertices, and sides, with auxiliary circles and trapezoids enriching the construction. ③Construction highlights: using Segment to create triangle sides, OrthogonalLine to draw altitudes through vertices perpendicular to opposite sides, Line and Intersect to find altitude intersections, and Angle to mark relevant angles; objects include vertices A, B, C, sides a, b, c, altitudes d, e, f, intersection points D, E, F, G, and angles α, β, γ, fully revealing the orthocenter's generation. ④Suitable for middle/high school geometry lessons, math lab activities, or self-study, helping learners grasp the definition of the orthocenter and the concurrency of altitudes, while dragging vertices to observe how the orthocenter moves, fostering dynamic geometric reasoning.