Special Right Triangles: 30°-60°-90° and 45°-45°-90° Constructions

① This GeoGebra example dynamically demonstrates the side-length ratios and angle relationships of special right triangles (30°-60°-90° and 45°-45°-90°), making their geometric properties visually intuitive. ② Core mathematical concepts include right triangles, special angles (30°, 45°, 60°), trigonometric ratios, similar triangles, and the Pythagorean theorem. ③ Construction highlights: using Segment to draw triangle sides, Rotate to generate specific angles, Angle to label angle measures, Ray to extend sides, and Dilate to adjust side lengths proportionally; key objects include points A, B, C, segments a, b, c, and angles α, β, γ, with precise control via rotation and scaling. ④ Suitable for upper middle school to high school students, ideal for classroom demonstrations, math labs, or self-study to grasp the side-length patterns of special right triangles and their applications in trigonometry.