Orthocenter Construction in a Right Triangle

This example demonstrates how to locate the orthocenter of a right triangle through a step-by-step geometric construction and visualize the key special property of right triangles. It centers on fundamental Euclidean geometry ideas: orthocenter (intersection of altitudes), altitudes as lines perpendicular to triangle sides, and finding their intersection via coordinate-free construction. Construction workflow uses GeoGebra commands such as Segment to define the triangle’s edges (points like A, B, C, D, E), OrthogonalLine to draw altitude lines perpendicular to the relevant sides, Intersect to compute the altitude intersection point (the orthocenter, e.g., h), Polygon to outline triangle-related regions or connect vertices, and Angle to express/verify angle conditions (symbols like α and β). The diagram-object setup (including auxiliary labeled objects and lines) is designed for interactive exploration. Suitable for middle/high school geometry, classroom demonstrations, and learners practicing synthetic construction with GeoGebra.