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梯形中位线性质探究

梯形中位线性质探究
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2017-01-23 01:12
多边形解析几何几何作图
①本范例演示梯形中位线的性质，即中位线平行于底边且等于两底边和的一半；②涉及核心数学概念：梯形、中位线、平行线、相等线段；③作图要点：使用Polygon、Midpoint、Segment、Distance、Angle、Point、Perimeter、PointIn等GeoGebra命令和对象构建梯形及中位线，并计算相关距离和角度；④适合初中及以上数学教学，用于直观理解梯形中位线定理。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Midpoint(A, B) → E
  3. Midpoint(C, D) → F
  4. Segment(E, F) → f
  5. Distance(A, E) → distanceAE
  6. Distance(E, B) → distanceEB
  7. Distance(C, F) → distanceCF
  8. Distance(F, D) → distanceFD
  9. Polygon(G, H, I, J) → poly2, g, h, i, j
  10. Midpoint(G, H) → K
  11. Midpoint(I, J) → L
  12. Segment(K, L) → k
  13. Angle(F, E, B) → α
  14. Angle(D, A, E) → β
  15. Angle(F, D, A) → γ
  16. Angle(C, F, E) → δ
  17. Polygon(M, N, O, P) → poly3, m, n, o, p
  18. Distance(M, N) → distanceMN
  19. Distance(P, O) → distancePO
  20. Midpoint(M, N) → R
  21. Distance(M, R) → distanceMR
  22. Distance(R, N) → distanceRN
  23. Point(m) → T
  24. Point(m) → U
  25. Midpoint(O, P) → Q
  26. Distance(O, Q) → distanceOQ
  27. Distance(Q, P) → distanceQP
  28. Perimeter(poly3) → perimeterpoly3
  29. PointIn(poly3) → Pointpoly3
  30. Segment(U, Q) → l
  31. Point(Circle[P, 5]) → V
  32. Segment(P, V) → q
  33. Distance(U, Q) → distanceUQ
  34. Midpoint(U, Q) →
  35. Distance(M, S) → distanceMS
  36. Midpoint(M, S) →