Rectangle Construction with Cosine, Dilation, and 3D Vectors

This example demonstrates how to construct a rectangle using geometric construction commands, and further illustrates its connections to cosine, dilation, square, three-dimensional vectors, and bar charts. The core mathematical concepts include the definition and properties of rectangles, the application of the cosine function in angle calculations, similarity transformations through dilation, and vector representation in 3D space. Construction highlights: using GeoGebra commands such as Line, OrthogonalLine, Point, Intersect, Polygon, and Angle, the example sequentially creates lines f, g, h, intersection points C and D, polygon poly1, sides b, c, d, a, and angles α, β, γ, δ. This example is suitable for middle and high school geometry instruction, helping students understand the rigorous steps of rectangle construction while extending to trigonometry, transformations, and vector applications. It also serves as a practical demonstration of multi-tool collaborative construction in GeoGebra.