Special Right Triangles: Dynamic Exploration of Side Ratios and Angles

① This GeoGebra example dynamically demonstrates the side-length ratios and angle relationships of special right triangles, such as 30°-60°-90° and 45°-45°-90° triangles. ② Core mathematical concepts include right triangles, special angles (30°, 45°, 60°), trigonometric ratios, the Pythagorean theorem, and geometric measurements (side lengths and distances). ③ Construction highlights: using commands like Line, Rotate, Angle, OrthogonalLine, Segment, Intersect, Distance, and Midpoint to build the triangle, generate perpendiculars, locate intersection points, and compute distances; Text objects display live measurements of side lengths, allowing users to verify the special triangle properties interactively. ④ Suitable for middle school to high school students learning right triangle properties, introductory trigonometry, or for teachers to use in classroom demonstrations to foster intuitive understanding of abstract ratio relationships.