Triangle Inscribed in a Rectangle: Geometric Construction and Angle Relations

①This example demonstrates how to construct a triangle inscribed within a rectangle and explore the angular relationships between its vertices, sides, and the rectangle's boundaries. ②Core mathematical concepts include inscribed polygons, perpendicular lines, angle measurement, and geometric constraints. ③Construction details: using GeoGebra commands such as Polygon to create the rectangle and triangle, Line and OrthogonalLine for perpendicular constructions, Intersect to find intersection points, and Angle to label key angles α, β, γ. Objects involved include D, E, F, poly2, f_1, d, e, j, k, l, m, G, n, A, B, C, and text1. ④Suitable for middle and high school geometry classes, this example helps students understand inscribed figure construction, perpendicularity, and angle calculations, and serves as an introductory dynamic geometry exploration.