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IM 6.1.8 Lesson: Triangle Area - Activity 2

IM 6.1.8 Lesson: Triangle Area - Activity 2
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2020-08-26 22:40
TrianglePolygonCoordinate GeometryGeometric Construction
In collections Grade 6 Unit 1: Area and Surface Area
This GeoGebra example demonstrates the construction of a triangle and the calculation of its area, illustrating the base‑height formula through interactive geometry. Core concepts include triangle area, geometric construction, and coordinate geometry with points and segments. The construction uses the Segment command to draw edges, the Polygon command to create the triangle polygon, and a CustomTriangle object for custom triangle definitions, involving vertices A, B, C and auxiliary points D, E, F, etc. It is suitable for middle‑school geometry lessons (grades 6‑8) and for teacher presentations or student exploration of triangle area properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Polygon(A, C, B) → t1, b, a, c
  5. Segment(D, E) → i
  6. Segment(E, F) → j
  7. Segment(F, G) → k
  8. Segment(G, D) → l
  9. Polygon(D, E, F, G) → q1, d, e, f_1, g_1
  10. Segment(H, I) → m
  11. Segment(I, J) → n
  12. Segment(J, K) → p
  13. Segment(K, L) → q
  14. Segment(L, H) → r
  15. Polygon(H, I, J, K, L) → poly1, h_1, i_1, j_1, k_1, l_1
  16. Segment(M, N) → s
  17. Segment(N, O) → t
  18. Segment(O, P) → m_1
  19. Segment(P, Q) → n_1
  20. Segment(Q, R) → p_1
  21. Segment(R, M) → q_1
  22. Polygon(R, M, N, O, P, Q) → poly2, r_1, m_2, n_2, o, p_2, q_2
  23. Segment(S, T) → s_1
  24. Segment(T, U) → t_1
  25. Segment(U, V) → a_1
  26. Segment(V, W) → b_1
  27. Segment(W, Z) → c_1
  28. Segment(Z, A_1) → d_1
  29. Segment(A_1, S) → e_1
  30. Polygon(S, T, U, V, W, Z, A_1) → poly3, s_2, t_2, u, v, w, z_1, f_2
  31. Segment(B_1, C_1) → g_2
  32. Segment(C_1, D_1) → h_2
  33. Segment(D_1, E_1) → i_2
  34. Segment(E_1, F_1) → j_2
  35. Segment(F_1, G_1) → k_2
  36. Segment(G_1, H_1) → l_2
  37. Segment(H_1, I_1) → r_2
  38. Segment(I_1, B_1) → a_2
  39. Polygon(B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1) → poly4, b_2, c_2, d_2, e_2, f_3, g_3, h_3, i_3
  40. Segment(J_1, K_1) → j_3
  41. Segment(K_1, L_1) → k_3
  42. Segment(L_1, M_1) → l_3
  43. Segment(M_1, N_1) → m_3
  44. Segment(N_1, O_1) → n_3
  45. Segment(O_1, P_1) → p_3
  46. Segment(P_1, Q_1) → q_3
  47. Segment(Q_1, R_1) → r_3
  48. Segment(R_1, J_1) → s_3
  49. Polygon(R_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1) → poly5, t_3, a_3, b_3, c_3, d_3, e_3, o_1, f_4, g_4
  50. Segment(S_1, T_1) → h_4
  51. Segment(T_1, U_1) → i_4
  52. Segment(U_1, V_1) → j_4
  53. Segment(V_1, W_1) → k_4
  54. Segment(W_1, Z_1) → l_4
  55. Segment(Z_1, A_2) → m_4
  56. Segment(A_2, B_2) → n_4
  57. Segment(B_2, C_2) → p_4
  58. Segment(C_2, D_2) → q_4
  59. Segment(D_2, S_1) → r_4
  60. Polygon(S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2) → poly6, s_4, e_4, t_4, u_1, v_1, w_1, a_4, b_4, c_4, d_4
  61. CustomTriangle(E_2, F_2, G_2) → f_5, g_5, h_5, t2
  62. CustomTriangle(H_2, I_2, J_2) → i_5, j_5, k_5, t3
  63. CustomTriangle(K_2, L_2, M_2) → l_5, m_5, n_5, t4
  64. CustomTriangle(N_2, O_2, P_2) → p_5, q_5, r_5, t5

AI Drawing Prompt Reference

In a coordinate plane, first draw a triangle by choosing three vertices and connecting them pairwise to form its three sides, then create the triangular polygon as a closed filled region. Next, inside (or near) the triangle, draw another closed quadrilateral polygon by constructing a connected boundary made from four consecutive vertices and joining them in order. After that, add a separate closed polygon region formed by five consecutive vertices connected by line segments in sequence. Finally, overlay an additional closed polygon region defined by eight consecutive vertices, connecting adjacent vertices with segments and closing the loop to complete the boundary.
The prompt above was compiled from the original drawing commands and is for reference only.