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NCTM Mathematics Teacher Calendar Problem (11-2-2016)

NCTM Mathematics Teacher Calendar Problem (11-2-2016)
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2016-11-06 09:32
TriangleTrigonometryGeometric Construction
In collections CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry Review Triangle Theorems
This example demonstrates a problem from NCTM's Mathematics Teacher magazine on November 2, 2016. It primarily involves triangles, angles, and trigonometry. The construction uses GeoGebra commands such as Line, Circle, and Polygon. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(C, B_1) → a
  2. OrthogonalLine(C, a) → d
  3. OrthogonalLine(B_1, a) → e
  4. Point(d) → C_1
  5. Ray(C, C_1) → c
  6. Point(d) → E
  7. Ray(C, E) → b
  8. Ray(C, B_1) → g
  9. Point(g) → F
  10. Ray(C, F) → h
  11. Point(h) → B
  12. Ray(C, E) → i
  13. Point(i) → A
  14. Midpoint(A, B) → M
  15. Segment(C, A) → j
  16. Segment(C, B) → k
  17. Circle(C, Min[(0.15 * j), (0.15 * k)]) → p
  18. Intersect(p, a, 2) → I
  19. Intersect(p, i, 1) → J
  20. Intersect(p, a, 1) → K
  21. CircleSector(C, J, K) → q
  22. Polygon(C, B, A) → poly1, h_1, a_1, g_1
  23. Rotate(q, If[0 < f ≤ 1, ((-f) * π / 2), -1.5707963267948966], C) → q'
  24. Dilate(B, If[1 < f ≤ 2, 2 - f, 0], M) → G'
  25. Rotate(B, If[2 < f ≤ 3, ((f - 2) * π), 3.141592653589793], M) → G'_1
  26. Rotate(G', If[2 < f ≤ 3, ((f - 2) * π), 3.141592653589793], M) → G''
  27. Angle(A, M, C) → α
  28. Rotate(G'_1, If[3 < f ≤ 4, ((f - 3) * α), α], M) → L
  29. Rotate(G'', If[3 < f ≤ 4, ((f - 3) * α), α], M) → G'''
  30. Rotate(B, 45°, C) → G'_2
  31. Angle(B, C, G'_2) → β
  32. Ray(C, G'_2) → m
  33. Segment(B, A) → n
  34. Intersect(m, n) → D
  35. OrthogonalLine(C, n) → r
  36. Intersect(r, n) → P
  37. Segment(C, P) → s
  38. Segment(C, M) → t
  39. Segment(C, D) → f_1
  40. Circle(P, (0.06 * n)) → c_1
  41. Intersect(c_1, s, 1) → O
  42. Intersect(c_1, n, 2) → P_1
  43. CircleSector(P, P_1, O) → d_1
  44. Dilate(C, If[1 < f ≤ 2, 2 - f, 0], D) → A'
  45. Segment(C, A') → l
  46. Circle(C, Radius[p]) → e_1
  47. Intersect(e_1, f_1) → Q,
  48. Intersect(e_1, j) → R,
  49. CircleSector(C, Q, R) → k_1
  50. Rotate(k_1, If[3 < f ≤ 4, ((-(f - 3)) * π / 4), ((-π)) / 4], C) → p_1
  51. Dilate(C, If[4.5 < f ≤ 5.5, 5.5 - f, 0], P) → A'_1
  52. Segment(C, A'_1) → i_1
  53. Rotate(d_1, If[6.25 < f ≤ 7.25, ((f - 6.25) * π / 2), π / 2], P) → q_1
  54. Dilate(B, If[8 < f ≤ 9, 9 - f, 0], M) → G'_3
  55. Rotate(B, If[9 < f ≤ 10, ((-(f - 9)) * π), (-π)], M) → G'_4
  56. Rotate(G'_3, If[9 < f ≤ 10, ((-(f - 9)) * π), (-π)], M) → S
  57. Dilate(A, If[8 < f ≤ 9, 9 - f, 0], M) → H'
  58. Segment(A, H') → j_1
  59. Angle(A, M, C) → γ
  60. Rotate(A, If[9 < f ≤ 10, ((f - 9) * γ), γ], M) → H'_1
  61. Rotate(H', If[9 < f ≤ 10, ((f - 9) * γ), γ], M) → H''
  62. Segment(H'_1, H'') → l_1
  63. Rotate(H'_1, If[10 < f ≤ 11, ((f - 10) * (π - γ)), π - γ], M) → T
  64. Rotate(H'', If[10 < f ≤ 11, ((f - 10) * (π - γ)), π - γ], M) → H'''
  65. Segment(T, H''') → m_1
  66. Intersect(e_1, s, 1) → U
  67. Intersect(e_1, f_1, 1) → V
  68. CircleSector(C, V, U) → r_1
  69. Angle(V, C, U) → δ
  70. Rotate(r_1, If[11.75 < f ≤ 12.75, ((-(f - 11.75)) * δ), (-δ)], C) → s_1
  71. Segment(A, P) → n_1
  72. Intersect(e_1, l, 1) → W
  73. Intersect(e_1, l_1, 1) → Z
  74. CircleSector(C, W, Z) → t_1
  75. Rotate(t_1, If[11.75 < f ≤ 12.75, ((-(f - 11.75)) * ((2 * π) - δ)), (-((2 * π) - δ))], C) → c_2

AI Drawing Prompt Reference

Draw a triangle with a point connected to its vertices. From this point, draw three perpendicular line segments. Then, draw a circle centered at the triangle's vertices and find its intersections with the triangle's sides. Use these intersections to create a sector and rotate it around the vertex. Finally, add some helper line segments and circles to complete the construction.
The prompt above was compiled from the original drawing commands and is for reference only.