Triangle to Rectangle: Equal-Area Transformation

This GeoGebra example demonstrates how to transform a triangle into a rectangle of equal area through geometric construction, visually linking the area formulas of triangles and rectangles. The core mathematical concepts include area equivalence, triangle and rectangle area formulas, perpendicular lines, midpoints, and symmetry. The construction uses GeoGebra commands such as Line, OrthogonalLine, Point, Polygon, LineBisector, Intersect, Segment, Mirror, and PointIn to build the triangle and auxiliary lines. By drawing altitudes, finding midpoints, and applying reflections, the triangle is dissected and reassembled into a rectangle with the same area. This is ideal for middle school geometry lessons, helping students grasp area formula derivation and the idea of area-preserving transformations, and can serve as an interactive visual aid for dynamic geometric exploration.