MathPlotAI Logo MathPlotAI

Angle Addition (Values Shown) via Rotation

Angle Addition (Values Shown) via Rotation
Loading the math board and drawing, please wait…
2021-01-23 12:21
CircleAngleTransformationGeometric ConstructionSlider Animation
This example visually demonstrates the angle addition principle by constructing a dynamic configuration where the sum of two angles matches the resulting composed angle, with the corresponding numerical values shown on the diagram. Key ideas include angle addition, geometric interpretation using circle arcs/sector markings, and tracking how rotating rays changes the measured angles during an animation. Construction in GeoGebra relies on: Rotate to rotate rays/objects around a reference point so that directions combine; Angle to compute and display the current angle measures (e.g., α, β, γ, δ, ε, ζ, η, θ and the composed/result angles); Circle and CircleSector to draw the supporting circle and angle sectors; and Segment to connect endpoints and clearly define the angle arms. Animation drives parameter changes so points/objects (such as A, B, C, D and their primed variants) update frame by frame, making the numeric angle values vary consistently with the geometric composition. Suitable for middle/high school geometry lessons and for students learning the geometric foundations behind angle addition and related trigonometric concepts.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Circle(C, D) → d
  3. Rotate(B, a°, A) → B'
  4. Angle(B, A, B') → α
  5. Rotate(D, b°, C) → D'
  6. Angle(D, C, D') → β
  7. Rotate(D, 30°, C) → D'_1
  8. Angle(D, C, D'_1) → γ
  9. Rotate(D'_1, 30°, C) → E
  10. Angle(D'_1, C, E) → δ
  11. Rotate(E, 30°, C) → E'
  12. Angle(E, C, E') → ε
  13. Rotate(E', 30°, C) → E''
  14. Angle(E', C, E'') → ζ
  15. Rotate(E'', 30°, C) → E'''
  16. Angle(E'', C, E''') → η
  17. Rotate(E''', 30°, C) → F
  18. Angle(E''', C, F) → θ
  19. Rotate(F, 30°, C) → F'
  20. Angle(F, C, F') → ι
  21. Rotate(F', 30°, C) → F''
  22. Angle(F', C, F'') → κ
  23. Rotate(F'', 30°, C) → F'''
  24. Angle(F'', C, F''') → λ
  25. Rotate(F''', 30°, C) → G
  26. Angle(F''', C, G) → μ
  27. Rotate(G, 30°, C) → G'
  28. Angle(G, C, G') → ν
  29. Rotate(B, 30°, A) → B'_1
  30. Angle(B, A, B'_1) → ξ
  31. Rotate(B'_1, 30°, A) → H
  32. Angle(B'_1, A, H) → ο
  33. Rotate(H, 30°, A) → H'
  34. Angle(H, A, H') → ρ
  35. Rotate(H', 30°, A) → H''
  36. Angle(H', A, H'') → σ
  37. Rotate(H'', 30°, A) → H'''
  38. Angle(H'', A, H''') → τ
  39. Rotate(H''', 30°, A) → I
  40. Angle(H''', A, I) → υ
  41. Rotate(I, 30°, A) → I'
  42. Angle(I, A, I') → ϕ
  43. Rotate(I', 30°, A) → I''
  44. Angle(I', A, I'') → χ
  45. Rotate(I'', 30°, A) → I'''
  46. Angle(I'', A, I''') → ψ
  47. Rotate(I''', 30°, A) → J
  48. Angle(I''', A, J) → ω
  49. Rotate(J, 30°, A) → J'
  50. Angle(J, A, J') → α_1
  51. Segment(A, B) → f
  52. Segment(A, B'_1) → g
  53. Segment(A, H) → h
  54. Segment(A, H') → i
  55. Segment(A, H'') → j
  56. Segment(A, H''') → k
  57. Segment(A, I) → l
  58. Segment(A, I') → m
  59. Segment(A, I'') → n
  60. Segment(A, I''') → p
  61. Segment(A, J) → q
  62. Segment(A, J') → r
  63. Segment(C, D) → s
  64. Segment(C, D'_1) → t
  65. Segment(C, E) → e
  66. Segment(C, E') → f_1
  67. Segment(C, E'') → g_1
  68. Segment(C, E''') → h_1
  69. Segment(C, F) → i_1
  70. Segment(C, F') → j_1
  71. Segment(C, F'') → k_1
  72. Segment(C, F''') → l_1
  73. Segment(C, G) → m_1
  74. Segment(C, G') → n_1
  75. CircleSector(A, B, B') → c_1
  76. CircleSector(C, D, D') → d_1
  77. Circle(K, L) → e_1
  78. Segment(K, L) → p_1
  79. Rotate(L, 30°, K) → L'
  80. Angle(L, K, L') → β_1
  81. Rotate(L', 30°, K) → L''
  82. Angle(L', K, L'') → γ_1
  83. Rotate(L'', 30°, K) → L'''
  84. Angle(L'', K, L''') → δ_1
  85. Rotate(L''', 30°, K) → M
  86. Angle(L''', K, M) → ε_1
  87. Rotate(M, 30°, K) → M'
  88. Angle(M, K, M') → ζ_1
  89. Rotate(M', 30°, K) → M''
  90. Angle(M', K, M'') → η_1
  91. Rotate(M'', 30°, K) → M'''
  92. Angle(M'', K, M''') → θ_1
  93. Rotate(M''', 30°, K) → N
  94. Angle(M''', K, N) → ι_1
  95. Rotate(N, 30°, K) → N'
  96. Angle(N, K, N') → κ_1
  97. Rotate(N', 30°, K) → N''
  98. Angle(N', K, N'') → λ_1
  99. Rotate(N'', 30°, K) → N'''
  100. Angle(N'', K, N''') → μ_1
  101. Segment(K, L') → q_1
  102. Segment(K, L'') → r_1
  103. Segment(K, L''') → s_1
  104. Segment(K, M) → t_1
  105. Segment(K, M') → a_1
  106. Segment(K, M'') → b_1
  107. Segment(K, M''') → f_2
  108. Segment(K, N) → g_2
  109. Segment(K, N') → h_2
  110. Segment(K, N'') → i_2
  111. Segment(K, N''') → j_2
  112. Rotate(L, (a + b)°, K) → L'_1
  113. Angle(L, K, L'_1) → ν_1
  114. CircleSector(K, L, L'_1) → c_2
  115. Circle(K, L) → d_2

AI Drawing Prompt Reference

Create a dynamic rotation diagram with two circles c and d, and a series of points B', D', D'_1, E, E', E'', E''', F, F', F'', F''', G, G', H, H', H'', H''', I, I', I'', I''', J generated by rotating points around a reference point. The angles α, β, γ, δ, ε, ζ, η, θ, ι, κ, λ, μ, ν, ξ, ο, ρ, σ, τ, υ, ϕ, χ, ψ, ω are formed by these points and change dynamically as they rotate, illustrating the angle addition principle.
The prompt above was compiled from the original drawing commands and is for reference only.