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Rhombus Properties Interactive Demo (G.GCO.10)

Rhombus Properties Interactive Demo (G.GCO.10)
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2019-06-27 04:27
PolygonAngleVectorTransformationGeometric Construction
① This example demonstrates the key properties of a rhombus through an interactive geometric construction, without relying on specific side lengths or angle measures. ② Core mathematical concepts include the definition of a rhombus, properties of diagonals (perpendicular bisectors), symmetry, rotation and translation transformations, and the use of coordinates and vectors in geometry. ③ Construction highlights: Based on the construction summary, commands such as Circle, Line, Intersect, Point, Segment, Polygon are used to build the base figure, while Rotate, Translate, Dilate, Vector create dynamic linked objects; Angle, CircleArc, CircleSector help visualize angles and arcs, resulting in a draggable interactive model. ④ Suitable for middle school geometry or high school introductory coordinate geometry, useful for exploring rhombus properties, understanding geometric transformations, and as a GeoGebra construction tutorial.

GeoGebra Commands & Parameters

  1. Circle(B, A) → f
  2. Circle(A, B) → c
  3. Line(A, B) → b
  4. Intersect(c, b, 2) → C
  5. CircleArc(A, B, C) → d
  6. Point(d) → D
  7. Segment(D, B) → s
  8. Circle(D, A) → e
  9. Intersect(e, f, 2) → E
  10. Segment(A, E) → n
  11. Intersect(n, s) → L
  12. Segment(A, B) → a
  13. Segment(A, D) → g
  14. Segment(D, E) → h
  15. Segment(E, B) → i
  16. Min(g, h) → j
  17. Dilate(B, If[0 < l ≤ 1, 1 - l, 0], A) → B'
  18. Segment(B, B') → m
  19. Angle(E, B, A) → α
  20. Angle(D, E, B) → β
  21. Rotate(B, If[1 < l ≤ 2, ((-(l - 1)) * α), α], B) → B'_1
  22. Rotate(B', If[1 < l ≤ 2, ((-(l - 1)) * α), (-α)], B) → B''
  23. Segment(B'_1, B'') → m'
  24. Rotate(B'_1, If[2 < l ≤ 3, ((-(l - 2)) * β), (-β)], E) → J
  25. Rotate(B'', If[2 < l ≤ 3, ((-(l - 2)) * β), (-β)], E) → B'''
  26. Segment(J, B''') → m''
  27. Rotate(J, If[3 < l ≤ 4, ((-(l - 3)) * α), (-α)], D) → J'
  28. Rotate(B''', If[3 < l ≤ 4, ((-(l - 3)) * α), (-α)], D) → K
  29. Segment(J', K) → m'''
  30. Circle(B, (0.2 * j)) → k
  31. Circle(E, (0.2 * j)) → p
  32. Intersect(p, m'', 1) → F
  33. Intersect(p, m', 1) → G
  34. Intersect(k, m', 1) → H
  35. Intersect(k, m, 1) → I
  36. CircleSector(B, H, I) → q
  37. CircleSector(E, F, G) → r
  38. Polygon(A, B, E, D) → poly1, a_1, b_1, e_1, d_1
  39. Dilate(B, If[5 < l ≤ 6, 6 - l, 0], D) → B'_2
  40. Vector(B, B'_2) → u
  41. Translate(q, u) → q'
  42. Rotate(q', If[6 < l ≤ 7, ((l - 6) * π), 3.141592653589793], D) → q''
  43. Dilate(E, If[7 < l ≤ 8, 8 - l, 0], A) → E'
  44. Vector(E, E') → v
  45. Translate(r, v) → r'
  46. Rotate(r', If[8 < l ≤ 9, ((-(l - 8)) * π), -3.141592653589793], A) → r''
  47. Dilate(D, If[9 < l ≤ 10, 10 - l, 0], L) → D'
  48. Vector(D, D') → w
  49. Min(n / 2, s / 2) → o
  50. Circle(L, (0.2 * o)) → t
  51. Intersect(t, s, 2) → M
  52. Intersect(t, n, 2) → N
  53. CircleSector(L, M, N) → c_1
  54. Segment(D, D') → f_1
  55. Dilate(L, If[10 < l ≤ 11, 11 - l, 0], B) → L'
  56. Circle(D, (0.2 * j)) → h_1
  57. Intersect(k, s) → P,
  58. Intersect(s, f_1) → Q
  59. Intersect(h_1, s, 1) → O
  60. Circle(A, (0.2 * j)) → k_1
  61. Intersect(k_1, m, 1) → R
  62. Intersect(k_1, n, 1) → S
  63. Intersect(k_1, m''', 1) → T
  64. Intersect(h_1, m'', 1) → U
  65. CircleSector(D, O, U) → q_1
  66. Dilate(A, If[11 < l ≤ 12, 12 - l, 0], L) → A'
  67. Segment(A, A') → i_1
  68. Dilate(L, If[12 < l ≤ 13, 13 - l, 0], E) → L'_1
  69. Segment(L, L'_1) → j_1
  70. Intersect(p, m'', 1) → V
  71. Intersect(p, n, 1) → W
  72. CircleSector(A, S, T) → s_1
  73. CircleSector(B, P, I) → p_1
  74. Intersect(p, m', 1) → Z
  75. CircleSector(E, W, Z) → r_1
  76. Segment(L, L') → g_1
  77. Rotate(L, If[13 < l ≤ 14, ((-(l - 13)) * π), -3.141592653589793], L) → L'_2
  78. Rotate(L', If[13 < l ≤ 14, ((-(l - 13)) * π), -3.141592653589793], L) → L''
  79. Segment(L'_2, L'') → l_1
  80. Rotate(L, If[14 < l ≤ 15, ((-(l - 14)) * π), 3.141592653589793], L) → L'_3
  81. Rotate(L'_1, If[14 < l ≤ 15, ((-(l - 14)) * π), 3.141592653589793], L) → A_1
  82. Segment(L'_3, A_1) → m_1
  83. Rotate(q_1, If[15 < l ≤ 16, ((-(l - 15)) * α / 2), ((-α)) / 2], D) → t_1
  84. Rotate(p_1, If[15 < l ≤ 16, ((-(l - 15)) * α / 2), ((-α)) / 2], B) → c_2
  85. Rotate(s_1, If[16 < l ≤ 17, ((-(l - 16)) * β / 2), ((-β)) / 2], A) → d_2
  86. Rotate(r_1, If[16 < l ≤ 17, ((-(l - 16)) * β / 2), ((-β)) / 2], E) → e_2
  87. Rotate(c_1, If[17 < l ≤ 18, ((l - 17) * π / 2), 1.5707963267948966], L) → f_2

AI Drawing Prompt Reference

Draw a draggable rhombus with four vertices formed by two intersecting equal circles and their centers. Start with two equal circles intersecting, connect their centers with a segment, take one intersection point as a vertex, pick another point on an arc as the fourth vertex, then connect all four vertices to form the rhombus. Show that diagonals are perpendicular bisectors, and add angle labels. Use a slider to sequentially demonstrate rotation about a vertex, translation, and scaling, highlighting corresponding parts with circular sectors, resulting in a complete interactive geometry demo.
The prompt above was compiled from the original drawing commands and is for reference only.