Orthocenter and Parabola Geometric Construction

This GeoGebra example demonstrates the construction of the orthocenter of a triangle and explores its relationship with a parabola. The core mathematical concepts include the orthocenter (intersection of the three altitudes), orthogonal lines, segments, angle measurement, and parabolic curves. The construction uses the Polygon command to create triangle ABC, OrthogonalLine to draw altitudes from each vertex to the opposite side, Intersect to find the orthocenter D, Segment to connect relevant points, and Angle to label interior angles α, β, γ. This example is suitable for high school or early college students to understand the definition and properties of the orthocenter, observe how its position changes for acute, right, or obtuse triangles, and investigate connections with conic sections. It serves as an interactive tool for geometry exploration and dynamic visualization.