Orthocenter Exploration: Dynamic Geometry Introduction

① This example demonstrates the concurrency of the three altitudes of a triangle at the orthocenter, and shows how the orthocenter's position changes as the triangle's vertices move. ② Core mathematical concepts include the definition of the orthocenter, altitude lines, perpendicularity, and the distinct locations of the orthocenter in acute, right, and obtuse triangles. ③ Construction highlights: from the construction summary, commands such as Rotate, Ray, Point, Polygon, Line, Segment, OrthogonalLine, Intersect, Dilate, and Angle are used to create triangle vertices A, B, C, construct altitudes via orthogonal lines, and determine the orthocenter D as their intersection, along with auxiliary circles, lines, and angle markers. ④ Suitable for middle or high school geometry lessons or student self-exploration, helping learners intuitively grasp the properties of the orthocenter and its relation to triangle shape, while also introducing dynamic geometry construction techniques.