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Properties of Rectangles and Rhombuses

Properties of Rectangles and Rhombuses
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2019-07-12 00:38
PolygonInequalityGeometric Construction
In collections Calculating areas as an approach to the notions of limit and
This example demonstrates the properties of rectangles and rhombuses, involving symmetry and similarity in geometry. Using GeoGebra commands such as Line, Intersect, and Midpoint, one can construct rectangles and rhombuses and explore their properties. Suitable for middle and high school students to learn geometric construction and property exploration.

GeoGebra Commands & Parameters

  1. Line(p, q) → f
  2. Intersect(c, f, 1) → A
  3. Intersect(c, f, 2) → C
  4. Line(C, xAxis) → g
  5. Intersect(c, g, 2) → B
  6. Midpoint(B, C) → D
  7. Intersect(c, yAxis) → E,
  8. Distance(D, E) → distantziaDE
  9. Circle(D, 0.28201) → d
  10. Circle(D, (0.28201 * 2)) → e
  11. Circle(D, (3 * 0.28201)) → h
  12. Circle(D, (4 * 0.28201)) → k
  13. Circle(D, (5 * 0.28201)) → r
  14. Circle(D, (6 * 0.280201)) → s
  15. Circle(D, (7 * 0.28201)) → t
  16. Circle(D, (8 * 0.28201)) → c_1
  17. Circle(D, (9 * 0.28201)) → d_1
  18. Intersect(d, yAxis, 2) → F
  19. Intersect(e, yAxis, 2) → G
  20. Intersect(h, yAxis, 2) → H
  21. Intersect(k, yAxis, 2) → I
  22. Intersect(t, yAxis, 2) → M
  23. Intersect(c_1, yAxis, 2) → N
  24. Intersect(d_1, yAxis, 2) → O
  25. Intersect(r, yAxis) → J, K
  26. Line(F, g) → i
  27. Line(G, i) → j
  28. Line(H, j) → l
  29. Line(I, l) → m
  30. Line(K, m) → n
  31. Intersect(c, i) → P, Q
  32. Intersect(c, j) → R, S
  33. Intersect(c, l) → T, U
  34. Intersect(c, m) → V, W
  35. Intersect(c, n) → Z, A_1
  36. OrthogonalLine(P, i) → i_1
  37. OrthogonalLine(R, j) → j_1
  38. OrthogonalLine(T, l) → k_1
  39. OrthogonalLine(V, m) → l_1
  40. OrthogonalLine(Z, n) → m_1
  41. OrthogonalLine(A_1, n) → e_1
  42. OrthogonalLine(W, m) → f_2
  43. OrthogonalLine(U, l) → g_2
  44. OrthogonalLine(S, j) → h_2
  45. OrthogonalLine(Q, i) → i_2
  46. Intersect(g, i_1) → J_1
  47. Intersect(g, i_2) → K_1
  48. Polygon(P, J_1, K_1, Q) → Laukia1, p_2, j_2, k_2, q_2
  49. Intersect(i, j_1) → L_1
  50. Intersect(i, h_2) → M_1
  51. Polygon(R, L_1, M_1, S) → Laukia2, r_2, l_2, m_2, s_2
  52. Intersect(j, k_1) → N_1
  53. Intersect(j, g_2) → O_1
  54. Polygon(T, N_1, O_1, U) → Laukia3, t_2, n_2, o_1, u
  55. Intersect(l, l_1) → P_1
  56. Intersect(l, f_2) → Q_1
  57. Polygon(V, P_1, Q_1, W) → Laukia4, v, a_2, b_2, w
  58. Intersect(m, m_1) → R_1
  59. Intersect(m, e_1) → S_1
  60. Polygon(Z, R_1, S_1, A_1) → Laukia5, z_1, c_2, d_2, e_2
  61. PointIn(Laukia1) → PuntuaLaukia1_1
  62. PointIn(Laukia2) → PuntuaLaukia2_1
  63. PointIn(Laukia3) → PuntuaLaukia3_1
  64. PointIn(Laukia4) → PuntuaLaukia4
  65. PointIn(Laukia5) → PuntuaLaukia5
  66. OrthogonalLine(B, j_2) → t_3
  67. Intersect(f, t_3) → F_2
  68. OrthogonalLine(F_2, t_3) → a_3
  69. Intersect(c, a_3, 2) → G_2
  70. Polygon(B, C, F_2) → Triangelua1, b_3, b_4, c_3
  71. Polygon(F_2, G_2, B) → Triangelua2, b_5, d_3, e_3
  72. Polygon(F_2, A, G_2) → Triangelua3, f_4, g_4, a_4
  73. PointIn(Triangelua1) → PuntuaTriangelua1
  74. PointIn(Triangelua2) → PuntuaTriangelua2
  75. PointIn(Triangelua3) → PuntuaTriangelua3
  76. Intersect(g, j_2) → H_2
  77. Intersect(g, j_2) → I_2
  78. Intersect(g, j_2) → J_2
  79. Intersect(g, k_2) → K_2
  80. Intersect(c, k_2, 1) → L_2
  81. Polygon(L_2, K_2, C) → Triangelua4, c_4, h_4, i_4
  82. Circle(D, (6 * 0.28201)) → d_4
  83. Intersect(d_4, yAxis) → L, B_1
  84. Distance(M, B_1) → distantziaMB1
  85. Line(B_1, n) → a
  86. Line(M, a) → b
  87. Line(N, b) → f_1
  88. Line(O, f_1) → g_1
  89. Intersect(c, a) → C_1, D_1
  90. Intersect(c, b) → E_1, F_1
  91. Intersect(c, f_1) → G_1, H_1
  92. OrthogonalLine(C_1, n) → h_1
  93. OrthogonalLine(E_1, a) → n_1
  94. OrthogonalLine(G_1, b) → p_1
  95. OrthogonalLine(H_1, f_1) → q_1
  96. OrthogonalLine(F_1, b) → r_1
  97. OrthogonalLine(D_1, a) → s_1
  98. Intersect(n, h_1) → I_1
  99. Intersect(n, s_1) → T_1
  100. Polygon(C_1, I_1, T_1, D_1) → Laukia6, t_1, a_1, b_1, f_3
  101. Intersect(a, n_1) → U_1
  102. Intersect(a, r_1) → V_1
  103. Polygon(E_1, U_1, V_1, F_1) → Laukia7, g_3, u_1, v_1, h_3
  104. Intersect(b, p_1) → W_1
  105. Intersect(b, q_1) → Z_1
  106. Polygon(G_1, W_1, Z_1, H_1) → Laukia8, i_3, w_1, j_3, k_3
  107. Line(E, g_1) → l_3
  108. Intersect(q_1, l_3) → A_2
  109. Intersect(p_1, l_3) → B_2
  110. PointIn(Laukia6) → PuntuaLaukia6
  111. PointIn(Laukia7) → PuntuaLaukia7
  112. PointIn(Laukia8) → PuntuaLaukia8
  113. Intersect(c, g_1) → C_2, D_2
  114. OrthogonalLine(C_2, g_1) → m_3
  115. OrthogonalLine(D_2, g_1) → n_3
  116. Intersect(m_3, l_3) → E_2
  117. Intersect(f_1, m_3) → M_2
  118. Intersect(f_1, n_3) → N_2
  119. Intersect(l_3, n_3) → O_2
  120. Polygon(E_2, M_2, N_2, O_2) → Laukia9, p_3, q_3, r_3, s_3
  121. PointIn(Laukia9) → PuntuaLaukia9
  122. PointIn(Laukia2) → PuntuaLaukia2
  123. PointIn(Laukia3) → PuntuaLaukia3
  124. PointIn(Laukia1) → PuntuaLaukia1
  125. PointIn(Triangelua4) → PuntuaTriangelua4
  126. Intersect(c, p_3) → P_2,
  127. Intersect(c, r_3) → Q_2,
  128. Polygon(P_2, M_2, N_2, Q_2) → Laukia10, l_4, m_4, n_4, p_4
  129. Intersect(s_3, p_3) → R_2
  130. Polygon(P_2, R_2, O_2, Q_2) → Laukia11, q_4, r_4, s_4, t_4
  131. PointIn(Laukia10) → PuntuaLaukia10
  132. PointIn(Laukia11) → PuntuaLaukia11