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Trapezoid Area and Median Line Demonstration

Trapezoid Area and Median Line Demonstration
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2017-11-07 15:22
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example dynamically demonstrates the relationship between a trapezoid's median line and its area, visually illustrating the trapezoid area formula. Key math concepts include trapezoid definition, median line properties, vector operations, and three-dimensional geometry. GeoGebra commands used in construction are point creation, polygon drawing, intersection calculation, and rotation transformation. Suitable for high school mathematics teaching, emphasizing the integration of spatial geometry and analytical geometry.

GeoGebra Commands & Parameters

  1. Point(Circle[F, 2]) → G
  2. Polygon(F, G, H, I, J, K) → poly2, f, g, h, i, j, k
  3. Point(Circle[L, 2]) → M
  4. Point(Circle[O, 1]) → P
  5. Intersect(k, j) → B
  6. Rotate(O, α, O) → O'
  7. Rotate(P, α, O) → P'
  8. Rotate(Q, α, O) → Q'
  9. Polygon(O', P', Q') → poly4', q', o', p'
  10. Rotate(L, (-β), B) → L'
  11. Rotate(M, (-β), B) → M'
  12. Rotate(N, (-β), B) → N'
  13. Polygon(L', M', N') → poly3', n', l', m'
  14. Intersect(m', j) → A
  15. Intersect(j, l') → C