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MATH 404 - Constructions

MATH 404 - Constructions
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2016-11-01 08:22
CirclePolygonAngleTransformationGeometric Construction
This GeoGebra example demonstrates a comprehensive set of geometric constructions, including circles, segments, polygons, lines, intersections, perpendiculars, midpoints, and angle bisectors. The core mathematical concepts involve classical geometric construction rules, parallel and perpendicular relationships, construction of polygons such as parallelograms and squares, and the visual representation of geometric transformations. The construction summary reveals the use of GeoGebra commands such as Circle, Segment, Polygon, Line, Intersect, OrthogonalLine, Point, LineBisector, and AngularBisector, with numerous objects labeled A through P, as well as named shapes like poly1, parallelogram, and square. This example is suitable for university-level mathematics courses (e.g., MATH 404) or advanced high school geometry, helping students understand the logical steps of geometric construction, relationships between figures, and precise construction techniques using dynamic geometry software.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(E, F) → h
  3. Polygon(G, H, I) → poly1, i, g_1, h_1
  4. Line(C, D) → f
  5. Line(J, f) → g
  6. Line(J, D) → j
  7. Line(C, j) → k
  8. Intersect(g, k) → K
  9. Polygon(K, J, D, C) → parallelogram, k_1, j_1, d, c_1
  10. Segment(L, M) → l
  11. OrthogonalLine(M, l) → m
  12. Point(m) → N
  13. Circle(M, L) → e
  14. Intersect(e, m, 2) → O
  15. OrthogonalLine(L, l) → n
  16. Circle(L, M) → p
  17. Intersect(p, n, 2) → P
  18. Polygon(P, O, M, L) → square, p_1, o, m_1, l_1
  19. Polygon(Q, R, S) → circumcenter, s, q, r
  20. LineBisector(Q, S) → t
  21. LineBisector(Q, R) → a
  22. Intersect(t, a) → T
  23. Circle(T, Q) → d_1
  24. Circle(U, V) → e_1
  25. Point(e_1) → W
  26. Circle(W, U) → f_1
  27. Intersect(e_1, f_1, 1) → Z
  28. Polygon(Z, U, W) → equilateral, w, z_1, u
  29. Circle(A_1, B_1) → q_1
  30. Point(q_1) → C_1
  31. Polygon(A_1, B_1, C_1) → isosceles, c_2, a_1, b_1
  32. Line(D_1, E_1) → b
  33. Line(F_1, b) → i_1
  34. Circle(D_1, E_1) → r_1
  35. Circle(E_1, D_1) → s_1
  36. Intersect(s_1, i_1, 1) → G_1
  37. Intersect(r_1, b) → H_1, I_1
  38. Intersect(r_1, i_1, 2) → J_1
  39. Intersect(s_1, b, 1) → K_1
  40. Polygon(D_1, E_1, J_1, G_1) → isosceles_1, d_2, e_2, j_2, g_2
  41. Polygon(L_1, M_1, N_1) → poly8, n_1, l_2, m_2
  42. AngularBisector(L_1, M_1, N_1) → t_1
  43. AngularBisector(N_1, L_1, M_1) → f_2
  44. AngularBisector(M_1, N_1, L_1) → h_2
  45. Intersect(t_1, f_2) → incenter
  46. Polygon(P_1, Q_1, R_1) → poly9, r_2, p_2, q_2
  47. LineBisector(P_1, R_1) → i_2
  48. LineBisector(Q_1, R_1) → k_2
  49. LineBisector(Q_1, P_1) → n_2
  50. Intersect(i_2, k_2) → circumcenter_1