Parallelogram Coordinate Geometry Construction and Properties

①This example demonstrates the construction of a parallelogram using coordinate geometry and explores its fundamental properties, such as opposite sides being parallel and equal, and diagonals bisecting each other. ②Core mathematical concepts include analytic geometry with vectors, point coordinates, segment lengths and directions, as well as polygon (parallelogram) characteristics. ③Construction highlights: using GeoGebra commands Vector, Point, Polygon, Segment, and Intersect to create vertices A, B, D, vector u, point C, sides a, b, c, d, diagonals f, g, and intersection point E, with text objects text1 to text4 displaying relevant measurements or relationships. ④Suitable for middle and high school students learning analytic geometry and plane geometry, useful for visually understanding coordinate-based proofs of geometric properties, and can serve as a classroom demonstration or self-exploration material for teachers and students.