Special Right Triangles: Geometric Construction and Angle Relations

This GeoGebra example demonstrates the construction of special right triangles (e.g., 30°-60°-90° and 45°-45°-90°) and their fixed side-length and angle ratios. Core math concepts include properties of right triangles, angle bisectors, perpendicular bisectors, polygon areas, and angle measurement. Construction highlights: using the Polygon command to create the initial triangle, Segment and LineBisector commands to draw auxiliary lines, Intersect to find key points, and Angle to label angles α, β, γ, etc. Multiple sub-triangles (poly2) are generated to reveal the internal division. Suitable for middle-to-high school students to intuitively grasp the side-angle relationships of special right triangles, and as a teaching example for geometric construction.