Exploring the Midsegment of a Trapezoid

This GeoGebra example demonstrates the key property of the midsegment (median) of a trapezoid: it is parallel to both bases and its length equals half the sum of the base lengths. The core mathematical concepts include trapezoid definition, midsegment theorem, parallel line properties, and proportional segment lengths. Construction uses GeoGebra commands such as Segment, Line, Point, Midpoint, and Intersect to build trapezoid ABCD, locate midpoints E and F of the legs, and connect them to form the midsegment. By dragging vertices, students can dynamically verify the invariant relationship. Suitable for middle school geometry lessons on trapezoid properties, and also serves as an introductory example for vector-based coordinate geometry in high school.