Special Right Triangles: 30°-60°-90° and 45°-45°-90° Geometric Construction

① This GeoGebra example dynamically demonstrates the special right triangles (30°-60°-90° and 45°-45°-90°), showing their side-length ratios and angle relationships in an interactive geometric environment. ② The core mathematical concepts include the properties of special right triangles, trigonometric ratios (e.g., sin30°=1/2, tan45°=1), and geometric transformations such as rotation and reflection. ③ Construction highlights: Based on the construction summary, the example uses commands like Segment, Rotate, Angle, Ray, Dilate, Line, and Mirror, involving multiple points (A, B, C, D, E, F, etc.) and segments (a, b, c, d, etc.). Rotations and reflections are used to create special angles, while dilation adjusts side lengths to achieve the desired proportions, resulting in a complete visual representation of the special triangles. ④ This resource is suitable for upper middle school or early high school students learning plane geometry and introductory trigonometry, and is also valuable for teachers to illustrate the memorization of special angle values and their geometric meaning.