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Rhombus and Square Demonstration

Rhombus and Square Demonstration
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2018-03-27 00:35
PolygonAngleCoordinate GeometryTransformationGeometric Construction
This example demonstrates the geometric properties and similarity transformations of rhombuses and squares. Key math concepts include polygons, angles, similarity transformations, and geometric constructions. The construction utilizes GeoGebra commands and objects such as Segment (line segment), Midpoint (midpoint), OrthogonalLine (perpendicular line), Line (line), LineBisector (angle bisector), Intersect (intersection), Point (point), Mirror (reflection), Polygon (polygon), Circle (circle), TableText (table text), Sum (sum), Distance (distance), InteriorAngles (interior angles), Angle (angle), and PointIn (point inside object). Suitable for middle school and above students to learn geometric transformations and polygon properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Midpoint(f) → C
  3. Segment(C, B) → f_2
  4. OrthogonalLine(C, f_2) → f_3
  5. Line(M, O) → p
  6. Line(N, p) → q
  7. Segment(M, N) → m
  8. LineBisector(m) → n
  9. Intersect(n, p) → B_1
  10. OrthogonalLine(B_1, p) → j_1
  11. Intersect(q, j_1) → C_1
  12. Segment(D_1, E_1) → k_1
  13. Point(f_3) → D
  14. Segment(C, D) → g
  15. Mirror(C, C) → C'
  16. Mirror(D, C) → D'
  17. Segment(C', D') → g'
  18. Polygon(A, D, B, D') → poly1, a_1, d_1, b_1, d'
  19. Polygon(E, F, G, H) → poly2, e_1, f_1, g_1, h
  20. Segment(F, H) → i
  21. LineBisector(i) → j
  22. Intersect(j, h) → K
  23. Intersect(f_1, j) → L
  24. Segment(E, G) → k
  25. LineBisector(k) → l
  26. Intersect(l, h) → I
  27. Intersect(f_1, l) → J
  28. Segment(E, F) → r
  29. Point(p) → P
  30. Point(q) → Q
  31. Intersect(n, q) → R
  32. Polygon(M, R, N, P) → poly3, m_1, r_1, n_1, p_1
  33. Segment(Q, R) → s
  34. Point(k_1) → S
  35. Segment(Q, M) → t
  36. Point(Circle[S, s]) → T
  37. Segment(S, T) → h_1
  38. OrthogonalLine(S, h_1) → i_1
  39. Circle(S, t) → c_1
  40. Intersect(c_1, i_1) → U, V
  41. Polygon(S, U, T) → poly4, t_1, s_1, u
  42. Intersect(p, p_1) → W
  43. Intersect(p, poly3) → Z, A_1
  44. Polygon(M, R, C_1, B_1) → poly5, m_2, r_2, c_2, b_2
  45. Point(q) → F_1
  46. Polygon(Q, C_1, B_1, M) → poly6, q_1, c_3, b_3, m_3
  47. Polygon(M, R, N, B_1) → poly7, m_4, r_3, n_2, b_4
  48. Intersect(m_4, r_3) → G_1
  49. Intersect(r_3, n_2) → H_1
  50. Segment(A, C) → l_1
  51. Segment(I_1, J_1) → g_2
  52. Midpoint(g_2) → K_1
  53. OrthogonalLine(K_1, g_2) → h_2
  54. Point(h_2) → L_1
  55. Segment(L_1, K_1) → i_2
  56. Segment(I_1, K_1) → j_2
  57. Segment(K_1, J_1) → k_2
  58. Mirror(L_1, K_1) → M_1
  59. Mirror(K_1, K_1) → N_1
  60. Segment(M_1, N_1) → l_2
  61. Circle(K_1, J_1) → d_2
  62. OrthogonalLine(K_1, j_2) → p_2
  63. Intersect(d_2, p_2) → O_1, P_1
  64. Polygon(L_1, I_1, M_1, J_1) → poly8, l_3, i_3, m_5, j_3
  65. Polygon(Q_1, R_1, S_1, T_1) → poly9, q_2, r_4, s_2, t_2
  66. Segment(Q_1, S_1) → a_2
  67. Segment(R_1, T_1) → e_2
  68. Intersect(a_2, e_2) → U_1
  69. TableText({{A1, B1, C1, D1, E1}, {A2, B2, C2, D2, E2}, {A3, B3, C3, D3, E3}, {A4, B4, C4, D4, E4}, {A5, B5, C5, D5, E5}, {A6, B6, C6, D6, E6}, {A7, B7, C7, D7, E7}, {A8, B8, C8, D8, E8}}, "|_") → text4
  70. Sum(B2:B8) → B9
  71. Sum(C2:C8) → C9
  72. Sum(D2:D8) → D9
  73. Sum(E2:E8) → E9
  74. Sum(B9:E9) → F9
  75. Distance(a_1, l_1) → o
  76. InteriorAngles(poly1) → α, β, γ, δ
  77. InteriorAngles(poly1) → ε, ζ, η, θ
  78. Angle(C, C', A) → ι
  79. Angle(A, C, D') → κ
  80. Angle(B, C, D) → λ
  81. Angle(A, C, D) → μ
  82. Angle(D', C, B) → ν
  83. Distance(r_3, m_4) → v
  84. PointIn(poly7) → Pointpoly7
  85. Angle(L_1, K_1, J_1) → ξ
  86. Angle(M_1, K_1, J_1) → ο
  87. InteriorAngles(poly8) → ρ, σ, τ, υ
  88. Angle(I_1, K_1, M_1) → ϕ
  89. Angle(I_1, K_1, L_1) → χ
  90. Polygon(L_1, K_1, J_1) → t1, j_4, l_4, k_3
  91. Polygon(M_1, K_1, J_1) → t2, j_5, m_6, k_4
  92. Polygon(I_1, K_1, M_1) → t3, m_7, i_4, k_5
  93. Polygon(I_1, L_1, K_1) → t4, k_6, i_5, l_5