Dynamic Construction of Rectangle and Rhombus with Geometric Relations

This GeoGebra example dynamically demonstrates the geometric relationships between rectangles and rhombuses, while also touching on conditional probability, statistics, line segments, derivatives, and 2D vectors. The core mathematical concepts include the right-angle property of rectangles, the equal-side property of rhombuses, and the use of auxiliary lines, perpendiculars, and circles to generate intersection points for studying transformations and metric relations. The construction uses commands such as Segment, Line, OrthogonalLine, Intersect, and Circle, creating objects A, B, C, D, E, F, G, H, I, along with auxiliary lines f, g, h, i, j, k, l, m, n, p, q, r and circles c, d, allowing dynamic adjustments to observe changes. It is suitable for middle and high school geometry teaching, math experiments, or teacher-made interactive courseware to help students intuitively understand properties of special quadrilaterals and geometric construction methods.