Midline Conjecture: Exploring Distances in a Triangle with an Inscribed Rectangl

① This GeoGebra example demonstrates a conjecture about the midline of a triangle by constructing a rectangle inside the triangle and measuring distances from its vertices to the triangle's sides and vertices. ② Core mathematical concepts include triangle midlines, midpoints, segment lengths, distance measurement, and geometric inequality conjectures, potentially linking arithmetic and geometric means. ③ Construction details: the Polygon command creates triangle poly1, Midpoint generates midpoints of sides, Segment connects midpoints to form the midline, and Distance computes key lengths such as DE, DB, CD, CA, EA, and EB, with Text objects displaying these values for dynamic observation. ④ Suitable for high school geometry classes or mathematical exploration activities, helping students discover properties of triangle midlines and verify conjectures, while also serving as a visual foundation for mean concepts in integral calculus.