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Identify Squares and Rectangles

Identify Squares and Rectangles
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2016-09-22 16:17
PolygonCoordinate GeometryGeometric Construction
In collections dps_bhavna Sorting Geometric Figures
This example demonstrates how to identify and classify squares and rectangles, and drag them into their respective grey boxes. It involves core mathematical concepts like polygon properties, geometric transformations, and analytical geometry. Construction highlights include commands/objects such as Polygon, Point, Rotate, Centroid, Ray, PointIn, Segment, Mirror, Line, Intersect, OrthogonalLine, and Circle. Suitable for middle school and above students for geometry recognition and classification practice.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  3. Polygon(I, J, 4) → poly3, n, p, q, r, K, L
  4. Polygon(M, N, 4) → poly4, s, t, c, d, O, P
  5. Point(xAxis) → Q
  6. Point(Circle[M_1, Segment[A_1, B_1]]) → N_1
  7. Rotate(N_1 + (Segment[B_1, C_1], 0), Angle[C_1 - B_1] + Angle[N_1 - M_1] - Angle[B_1 - A_1], N_1) → O_1
  8. Rotate(O_1 + (Segment[C_1, D_1], 0), Angle[D_1 - C_1] + Angle[O_1 - N_1] - Angle[C_1 - B_1], O_1) → P_1
  9. Polygon(M_1, N_1, O_1, P_1) → poly10, m_1, n_1, o_1, p_1
  10. Point(Circle[Q_1, Segment[U, V]]) → R_1
  11. Rotate(R_1 + (Segment[V, W], 0), Angle[W - V] + Angle[R_1 - Q_1] - Angle[V - U], R_1) → S_1
  12. Rotate(S_1 + (Segment[W, Z], 0), Angle[Z - W] + Angle[S_1 - R_1] - Angle[W - V], S_1) → T_1
  13. Polygon(Q_1, R_1, S_1, T_1) → poly11, q_2, r_2, s_2, t_2
  14. Point(Circle[U_1, Segment[Q, R]]) → V_1
  15. Rotate(V_1 + (Segment[R, S], 0), Angle[S - R] + Angle[V_1 - U_1] - Angle[R - Q], V_1) → W_1
  16. Rotate(W_1 + (Segment[S, T], 0), Angle[T - S] + Angle[W_1 - V_1] - Angle[S - R], W_1) → Z_1
  17. Polygon(U_1, V_1, W_1, Z_1) → poly12, u_1, v_1, w_1, z_2
  18. Point(Circle[E_1, 1]) → F_1
  19. Polygon(E_1, F_1, G_1, H_1) → poly5, e_1, f_1, g_1, h_1
  20. Centroid(poly1) → I_1
  21. Centroid(poly2) → J_1
  22. Centroid(poly3) → K_1
  23. Centroid(poly10) → L_1
  24. Centroid(poly11) → A_2
  25. Centroid(poly12) → B_2
  26. Point(Circle[Q_2, 1.4821605850919128]) → R_2
  27. Point(Circle[U_2, 1.4598630072715726]) → V_2
  28. Point(Circle[A_3, 1.1415778554264275]) → B_3
  29. Point(Circle[E_3, 0.6596969000988258]) → F_3
  30. Point(Circle[I_3, 1]) → J_3
  31. Ray((0, 0), (1, 0)) → i_1
  32. Point(e) → M_3
  33. Point(e) → N_3
  34. Polygon(M_3, N_3, O_3, P_3) → poly14, m_3, n_3, o_3, p_3
  35. PointIn(poly14) → Q_3
  36. Point(Circle[Q_3, 1]) → R_3
  37. Segment(Q_3, R_3) → j_1
  38. Mirror(R_3, Q_3) → S_3
  39. Point(Circle[R_3, 2]) → T_3
  40. Segment(R_3, T_3) → k_1
  41. Line(T_3, S_3) → l_1
  42. Line(R_3, l_1) → a_1
  43. Line(S_3, k_1) → b_1
  44. Intersect(a_1, b_1) → U_3
  45. Polygon(T_3, R_3, U_3, S_3) → poly15, t_3, r_3, u_3, s_3
  46. PointIn(poly14) → V_3
  47. Point(Circle[V_3, 2]) → W_3
  48. Segment(V_3, W_3) → q_1
  49. Line(W_3, V_3) → r_1
  50. Point(r_1) → Z_3
  51. OrthogonalLine(V_3, q_1) → s_1
  52. Circle(V_3, Z_3) → c_1
  53. Intersect(c_1, s_1) → A_4, B_4
  54. Polygon(W_3, B_4, Z_3, A_4) → poly6, w_3, b_4, z_3, a_4
  55. PointIn(poly14) → C_4
  56. Point(Circle[C_4, 0.6]) → D_4
  57. Segment(C_4, D_4) → t_1
  58. OrthogonalLine(D_4, t_1) → d_1
  59. Mirror(D_4, C_4) → E_4
  60. Line(E_4, d_1) → f_2
  61. Circle(D_4, E_4) → c_2
  62. Intersect(c_2, d_1) → F_4, G_4
  63. Circle(E_4, C_4) → d_2
  64. Intersect(d_2, f_2) → H_4, I_4
  65. Polygon(F_4, G_4, I_4, H_4) → poly9, f_4, g_4, i_4, h_4
  66. PointIn(poly14) → J_4
  67. Point(Circle[J_4, 2]) → K_4
  68. Segment(J_4, K_4) → g_2
  69. Point(Circle[J_4, 1]) → L_4
  70. Segment(J_4, L_4) → h_2
  71. Point(Circle[J_4, 1.5]) → M_4
  72. Segment(J_4, M_4) → i_2
  73. Point(Circle[J_4, 0.9]) → N_4
  74. Segment(J_4, N_4) → j_2
  75. Polygon(M_4, K_4, L_4, N_4) → poly8, m_4, k_4, l_4, n_4
  76. PointIn(poly14) → O_4
  77. Point(Circle[O_4, 2]) → P_4
  78. Segment(O_4, P_4) → k_2
  79. Point(Circle[O_4, 1.5]) → Q_4
  80. Segment(O_4, Q_4) → l_2
  81. Point(Circle[O_4, 1]) → R_4
  82. Segment(O_4, R_4) → m_2
  83. Point(Circle[O_4, 0.7]) → S_4
  84. Segment(O_4, S_4) → n_2
  85. Polygon(P_4, R_4, Q_4, S_4) → poly13, p_4, r_4, q_4, s_4

AI Drawing Prompt Reference

Draw a geometry practice figure with multiple squares and rectangles. Start by creating four squares of different sizes at various positions. Then construct three parallelograms using rotation based on a side and angle. Add a circle with a center and radius, and place a square on it. Mark centroids for each polygon. Finally, pick a random point inside one square, draw a circle around it, and use reflection and rotation to form a rhombus; also pick a point in another square and draw a circle. The layout is for identifying and classifying squares and rectangles.
The prompt above was compiled from the original drawing commands and is for reference only.