Rectangle Properties: Sides, Diagonals, Angles, and Area

This interactive GeoGebra example dynamically demonstrates the fundamental properties of a rectangle, including opposite sides parallel and equal, all four interior angles being right angles, diagonals equal in length and bisecting each other, and the relationship between side lengths and area. Core mathematical concepts covered are polygons, parallel and perpendicular lines, angles, segment lengths, area calculation, and geometric inequalities. The construction uses GeoGebra commands such as Line, OrthogonalLine, Polygon, PointIn, Point, AngularBisector, Segment, Intersect, Corner, and Angle to build rectangle ABCD, an interior point M, diagonal intersections, angle bisectors, auxiliary segments, and multiple angle markers. Users can drag points or use sliders to resize the rectangle and observe real-time updates of side lengths, angles, and area. Suitable for middle school to high school students learning plane geometry, and useful for teachers demonstrating rectangle properties or for students exploring relationships among rectangles, squares, and rhombi, as well as introductory optimization concepts under linear constraints.