Rotations: Dynamic Exploration of Lines, Triangles, and Optimization

① This GeoGebra example dynamically demonstrates the rotation of line segments, triangles, and straight lines around a point, linking to optimization problems involving angle changes. ② Core mathematical concepts include rotation transformations, linear equations, similar triangles, linear equations, and optimization, emphasizing invariants and positional relationships before and after rotation. ③ Construction highlights: Segment creates segments, Rotate applies to points A, B, C, etc., Angle defines rotation angles α, β, γ, generating rotated objects (A', B', f', etc.), while auxiliary lines i, j, k, l, m, n help analyze geometric relations. ④ Suitable for middle/high school geometry teaching, math labs, or competition training, aiding intuitive understanding of rotation properties and geometric optimization.