Constructing the Orthocenter of a Triangle by Amanda

This GeoGebra example demonstrates the dynamic construction of the orthocenter of a triangle, visually illustrating the concurrency of the three altitudes at a single point H. The core mathematical concepts covered include triangle geometry, altitudes, perpendicular lines, orthocenter, and triangle centers. Construction highlights: the Polygon command is used to create triangle poly1 from vertices A, B, and C; the OrthogonalLine command constructs altitudes relative to the triangle’s sides and auxiliary lines a, b, c, d; points D, E, F, G, H, I and objects c_1, a_1, b_1, f, g, h, i, j, k, l support the step-by-step geometric construction and intersection calculations. This resource is suitable for middle school and high school geometry instruction, triangle center exploration, and interactive classroom demonstrations.