积极 AI Logo 积极 AI

平行四边形面积演示 by Mark Dabbs

平行四边形面积演示 by Mark Dabbs
几何画板及绘图内容加载中，请稍等……
2014-09-22 23:24
多边形三角函数解析几何积分几何作图
①本范例演示平行四边形面积的计算方法，通过可视化方式展示底乘以高。②涉及核心数学概念包括平行四边形、面积公式、相似三角形、解析几何。③作图要点：使用 GeoGebra 命令如 Point, OrthogonalLine, Segment, Line, Intersect, Polygon, Dilate, Circle；对象包括 Translate, g, A, a, C, B_1, b, c, d, D_1, e, f, h, i, j, B, D, k, E, l, m, n, F, p, poly1, a_1, e_1, f_1, d_1, poly2, e_2, c_1, b_1, f_2, q, r, s, C', t, g_1。④适合初中及以上学生学习平行四边形面积公式及几何作图。

GeoGebra 命令及参数

  1. Point(g) → A
  2. OrthogonalLine(A, g) → a
  3. Point(g) → C
  4. Segment(C, B_1) → b
  5. Line(A, b) → c
  6. Line(B_1, g) → d
  7. Intersect(c, d) → D_1
  8. Segment(D_1, B_1) → e
  9. Segment(A, D_1) → f
  10. OrthogonalLine(C, g) → h
  11. OrthogonalLine(D_1, g) → i
  12. OrthogonalLine(B_1, g) → j
  13. Intersect(g, i) → B
  14. Intersect(g, j) → D
  15. Segment(If[x(B) ≥ x(A), B, A], If[x(B) ≥ x(A), C, D]) → k
  16. Point(k) → E
  17. Segment(A, B) → l
  18. Segment(C, D) → m
  19. OrthogonalLine(E, e) → n
  20. Intersect(n, e) → F
  21. Segment(F, E) → p
  22. Polygon(A, E, F, D_1) → poly1, a_1, e_1, f_1, d_1
  23. Polygon(E, C, B_1, F) → poly2, e_2, c_1, b_1, f_2
  24. Segment(B_1, F) → q
  25. Segment(F, D_1) → r
  26. Segment(A, C) → s
  27. Dilate(C, Translate, A) → C'
  28. Line(C', b) → t
  29. Line(B_1, s) → g_1
  30. Intersect(t, g_1) → G
  31. Circle(G, Segment[D_1, F]) → h_1
  32. Circle(C', Segment[A, E]) → k_1
  33. Line(A, C) → i_1
  34. Intersect(k_1, i_1) → H, I
  35. Intersect(h_1, g_1) → J, K
  36. Segment(B_1, K) → j_1
  37. Segment(K, I) → l_1
  38. Segment(I, C') → m_1
  39. Segment(G, C') → n_1
  40. Polygon(C', G, K, I) → poly3, c', g_2, k_2, i_2
  41. Segment(E, C) → p_1
  42. Segment(G, F) → q_1
  43. Segment(F, E) → r_1
  44. Segment(I, K) → s_1