Orthocenter! Dynamic Construction of Triangle Altitudes

① This GeoGebra example dynamically demonstrates the orthocenter of a triangle, the common intersection point of its three altitudes, and shows how its position changes for acute, right, and obtuse triangles. ② The core mathematical concept is the orthocenter, one of the triangle's five centers, involving perpendicular lines, intersections, and the relationship between altitudes and triangle shape. ③ Construction details: using the Polygon command to create triangle ABC (poly1), Line to draw sides, OrthogonalLine to construct altitudes from each vertex to the opposite side (lines d, e, f), and Intersect to find the foot points (D_1, D, E) and the orthocenter H. Dragging vertices A, B, C reveals the dynamic behavior. ④ Suitable for middle and high school students learning triangle geometry, and useful for teachers in classroom demonstrations or for self-exploration to understand how the orthocenter relates to triangle types.