Altitudes and Orthocenter of a Triangle by Brian Meeron

① This example demonstrates the geometric construction and properties of the three altitudes of an arbitrary triangle and their common intersection point, the orthocenter. ② Core mathematical concepts include altitudes, orthocenter, pedal triangle, angle relationships, and distances from the orthocenter to vertices and sides, along with symmetry and geometric inequalities. ③ Construction details: Using GeoGebra commands such as Segment, OrthogonalLine, Intersect, Angle, and Distance, the triangle ABC is built with its three altitudes, the feet D, E, F are marked, and the orthocenter H is found; auxiliary segments, angles α, β, γ, and distances like distanceIORTHOCENTER and distanceORTHOCENTERC are measured, with color-coded elements (green, red, blue). ④ Suitable for middle and high school geometry classes, this interactive figure helps students visualize the existence and location of the orthocenter (inside for acute triangles, at a vertex for right triangles, outside for obtuse triangles) and explore metric relationships, as well as connections to the circumcenter, centroid, and incenter.