Luera Investigation - Diagonals of a Rectangle

This GeoGebra example dynamically explores the properties of the diagonals of a rectangle, demonstrating that they are equal in length and bisect each other, while also revealing the triangular regions formed by the diagonals. Core mathematical concepts include rectangle definitions, diagonal properties, congruent and isosceles triangles, and an introductory connection to conditional probability through area ratios. The construction uses GeoGebra commands such as Segment, Line, OrthogonalLine, and Intersect to build rectangle vertices A, B, C, D, draw diagonals and perpendiculars, and mark intersection point E for observation. Suitable for middle school geometry lessons or high school review, this interactive tool helps students visualize symmetry and bisection, and can be extended to discuss probability and area comparisons.