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Fill Missing Polygons

Fill Missing Polygons
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2016-03-25 09:48
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to fill in missing polygons within a given figure. It involves core mathematical concepts such as polygons, equations, quadratic functions, quadratic equations, volume, and piecewise functions. The construction utilizes GeoGebra commands and objects like Point and Polygon. It is suitable for high school students learning geometric constructions.

GeoGebra Commands & Parameters

  1. Point(Circle[A_3, 4.7976730919163675]) → B_3
  2. Polygon(A_3, B_3, C_3, D_3) → Trapezoid_4, a_3, b_3, c_3, d_3
  3. Point(Circle[E_3, 4.008975512666096]) → F_3
  4. Polygon(E_3, F_3, G_3) → Triangle_{14}, g_3, e_3, f_3
  5. Point(Circle[H_3, 4.657552104464272]) → I_3
  6. Polygon(H_3, I_3, J_3) → Triangle_{11}, j_3, h_3, i_3
  7. Point(Circle[N_3, 1.5736493301325478]) → O_3
  8. Polygon(N_3, O_3, P_3) → poly5, p_3, n_3, o_3
  9. Point(Circle[Q_3, 2.8217615307867993]) → R_3
  10. Polygon(Q_3, R_3, S_3) → Triangle_{13}, s_3, q_3, r_3
  11. Point(Circle[T_3, 2.7221878484049857]) → U_3
  12. Polygon(T_3, U_3, V_3) → Triangle_{12}, v_3, t_3, u_3
  13. Point(Circle[W_3, 0.7726653838316267]) → Z_3
  14. Polygon(W_3, Z_3, A_4, B_4) → Rectangle_8, w_3, z_4, a_4, b_4
  15. Point(Circle[G_4, 1.515674330327962]) → H_4
  16. Polygon(G_4, H_4, I_4, J_4) → Rectangle_{10}, g_4, h_4, i_4, j_4
  17. Point(Circle[K_4, 1.5445367293641927]) → L_4
  18. Polygon(K_4, L_4, M_4, N_4) → Rectangle_9, k_4, l_4, m_4, n_4
  19. Point(Circle[O_4, 2.1450128079449797]) → P_4
  20. Polygon(O_4, P_4, Q_4, R_4) → Rectangle_{11}, o_4, p_4, q_4, r_4
  21. Point(Circle[S_4, 4.851998817260502]) → T_4
  22. Polygon(S_4, T_4, U_4, V_4) → Trapezoid_1, s_4, t_4, u_4, v_4
  23. Point(Circle[W_4, 3.3173249493970496]) → Z_4
  24. Polygon(W_4, Z_4, A_5) → Triangle_{15}, a_5, w_4, z_5
  25. Point(Circle[B_5, 1.540029445803641]) → C_5
  26. Polygon(B_5, C_5, D_5) → Triangle_{16}, d_5, b_5, c_5
  27. Point(Circle[E_5, 1.7265485382613106]) → F_5
  28. Polygon(E_5, F_5, G_5) → Triangle_{17}, g_5, e_5, f_5
  29. Point(Circle[H_5, 2.0257943441764636]) → I_5
  30. Polygon(H_5, I_5, J_5) → Triangle_5, j_5, h_5, i_5
  31. Point(Circle[C, 0.7149407218528125]) → D
  32. Polygon(C, D, K_3, L_3) → Rectangle_2, c, d, k_3, l_3
  33. Point(Circle[M_3, 5.661174939405696]) → D_4
  34. Polygon(M_3, D_4, E_4) → Triangle_1, e_4, m_3, d_4
  35. Point(Circle[P, 4.225628205665061]) → Q
  36. Polygon(P, Q, R, S) → Trapezoid_3, p, q, r, s
  37. Point(Circle[T_1, 1.086478133653952]) → U_1
  38. Polygon(T_1, U_1, F_2, C_4) → Trapezoid, t_1, u_1, f_2, c_4
  39. Point(Circle[Rectangle_4, 1.4722769097943167]) → K_5
  40. Polygon(Rectangle_4, K_5, L_5, M_5) → Rectangle, f_4, k_5, l_5, m_5
  41. Point(Circle[A, 3.366194046238461]) → B
  42. Polygon(A, B, E) → Triangle, e, a, b

AI Drawing Prompt Reference

Draw a figure containing multiple polygons and rectangles. Start by drawing a circle and taking a point A_3 on it. Then, draw a trapezoid with A_3 as one of its vertices. Continue by drawing circles and points, connecting them to form triangles, rectangles, and trapezoids. Finally, draw a triangle and a rectangle, ensuring all polygons and rectangles are connected to form a complete figure.
The prompt above was compiled from the original drawing commands and is for reference only.