Sliding Trigon: Dynamic Triangle Transformations and Intersection Exploration

①This example demonstrates a sliding triangle (Sliding trigon) that moves dynamically on the plane, allowing users to drag or use sliders to change its position and shape, and observe how geometric elements such as vertices, sides, midpoints, and the orthocenter evolve and interact. ②Core mathematical concepts include triangle geometry (orthocenter, midpoints, altitudes), polygon construction, circle intersections, and the integration of functions and equations in geometric contexts, along with elements of probability and polynomials for a cross-disciplinary approach. ③Construction highlights: Based on the summary, the GeoGebra commands used include Polygon to create triangle poly1, Midpoint for midpoints, Segment for edges, Intersect for intersection points, Circle for circles, and Point for key points; objects include vertices A, B, C, sides a, b, c, midpoints D, E, F, and numerous auxiliary points (G, H, J, M, N, etc.) plus text labels (text1, text2, text3), with sliding achieved via sliders or dragging. ④Suitable for upper secondary to early university students in geometry and algebra courses, useful for exploring dynamic triangle properties, geometric transformations, and locus problems, as well as a model for interactive lesson design.