Constructing the Orthocenter of an Obtuse Triangle

This GeoGebra example demonstrates how to construct the orthocenter of an obtuse triangle and visualize where it lies relative to the triangle (notably, the orthocenter moves outside the triangle in the obtuse case). It focuses on core geometry ideas: the definition of the orthocenter as the intersection of the three altitudes, the properties of perpendicular lines, and the angle relationships that guide the construction. Construction outline: Polygon is used to build triangle ABC; Angle sets up the relevant angle information for the configuration; OrthogonalLine draws the altitudes from vertices to the opposite sides; and Intersect computes the intersection point(s) of these altitudes to obtain the orthocenter and related auxiliary points. Suitable for secondary-level Euclidean geometry instruction, GeoGebra-based geometry construction lessons, and student exploration of how changing triangle shape affects the orthocenter’s position.