Richard Orthocenter: Dynamic Exploration of Triangle Orthocenter and Parametric

This GeoGebra example dynamically demonstrates the construction of the orthocenter of a triangle and its associated geometric properties, incorporating parametric curves and symmetry to explore the locus and logical relationships as the triangle changes. Core mathematical concepts include the orthocenter (intersection of altitudes), orthogonal lines, similar triangles, rational number ratios, and symmetry. Construction highlights: using Polygon to create triangle ABC, Circle and Intersect for auxiliary circles and points, Line and OrthogonalLine for altitudes, Angle and Segment for angle and segment labeling, and multiple points (D, E, F, G, H, I, J, K, L, M, N, O, P, Q) along with parametric curves (k, l, m) to visualize dynamic variations. Suitable for high school geometry, math competition training, or introductory college geometry, this example helps students intuitively grasp orthocenter properties and logical reasoning in geometric construction.