Dynamic Construction and Properties of the Orthocenter of a Triangle by bailee

This GeoGebra example demonstrates the geometric fact that the three altitudes of a triangle are concurrent at the orthocenter. It visually shows how the orthocenter changes as the triangle's vertices move. The core mathematical concepts include the definition of an altitude, the concurrency of altitudes, and the relationship between the orthocenter and the triangle's angles. The construction uses the Polygon command to create triangle ABC, OrthogonalLine to draw perpendiculars from each vertex to the opposite side, Intersect to find the feet of the altitudes, and Segment to form the altitude segments. The Angle command is used to label angles α, β, γ, and a text object is added for explanation. This example is suitable for middle school to high school students learning about triangle centers, and for teachers demonstrating geometric constructions or exploring the orthocenter's position for acute, right, and obtuse triangles.