Trapezium Diagonals Midpoints

This GeoGebra example demonstrates the geometric property of the segment connecting the midpoints of the two diagonals in a trapezium (trapezoid). The core mathematical concepts involve the properties of trapezium diagonals, the midpoint theorem, and the proportionality of segments in parallel lines. Construction steps: use the Point command to create vertices A, B, C, D; Line to form sides; Polygon to construct the trapezium poly1; Segment to draw diagonals a_1 and c; Midpoint to locate E and F as the midpoints of the diagonals; finally Segment to connect E and F as line g. By dragging vertices, one can observe that the midpoint segment remains parallel to the bases and its length equals half the difference of the base lengths. Suitable for upper middle school or high school geometry classes, this interactive construction helps students intuitively grasp the generalized trapezium midline theorem and serves as a rich exploratory activity.