Rectangle Madness: A GeoGebra Example

Draw a rectangle and illustrate its geometric transformations and properties. Construct key points such as the orthocenter within or on the rectangle, and use trigonometric relationships to mark angles. Through combinatorial and similarity transformations, show the rectangle in different positions or rotations, highlighting its symmetry and proportional relations. Include clear auxiliary lines, such as altitudes or medians, to demonstrate the connection between the orthocenter and trigonometry. The overall composition should suit high school geometry education, intuitively showing the invariant properties of the rectangle under transformations.