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Angle Addition Formula Without Measures

Angle Addition Formula Without Measures
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2015-09-10 09:26
AngleVectorTrigonometryGeometric Construction
This example dynamically demonstrates the geometric meaning of the angle addition formula by combining two angles. It involves core math concepts like angle synthesis, vector addition, and geometric transformations. Constructed using GeoGebra commands such as Line, Point, Segment, Rotate, and Angle, it visually represents the dynamic synthesis of angles. Suitable for high school mathematics teaching to help students understand the angle addition formula and its applications.

GeoGebra Commands & Parameters

  1. Line(C_1, E_1) → a
  2. Point(Circle[F_1, 4]) → G_1
  3. Segment(F_1, G_1) → b
  4. Rotate(G_1, 45*°, F_1) → E1
  5. Angle(G_1, F_1, E1) → α
  6. Segment(F_1, E1) → c
  7. Point(Circle[Z, 4]) → A1
  8. Segment(Z, A1) → d
  9. Point(Circle[C1, 4]) → B1
  10. Segment(C1, B1) → e
  11. Point(Circle[K, 4]) → L
  12. Segment(K, L) → f
  13. Point(Circle[Q, 4]) → R
  14. Segment(Q, R) → g
  15. Point(Circle[H, 4]) → I
  16. Segment(H, I) → h
  17. Point(Circle[W, 4]) → X
  18. Segment(W, X) → i
  19. Point(Circle[T, 4]) → U
  20. Segment(T, U) → j
  21. Point(Circle[E, 4]) → F
  22. Segment(E, F) → k
  23. Rotate(I, 45*°, H) → G
  24. Angle(I, H, G) → β
  25. Rotate(A1, 90*°, Z) → Y
  26. Angle(A1, Z, Y) → γ
  27. Rotate(B1, 135*°, C1) → D1
  28. Angle(B1, C1, D1) → δ
  29. Rotate(L, 180*°, K) → J
  30. Angle(L, K, J) → ε
  31. Rotate(U, 30*°, T) → S
  32. Angle(U, T, S) → ζ
  33. Rotate(X, 15*°, W) → V
  34. Angle(X, W, V) → η
  35. Rotate(R, 60*°, Q) → P
  36. Angle(R, Q, P) → θ
  37. Rotate(F, 75*°, E) → D
  38. Angle(F, E, D) → ι
  39. Segment(H, G) → l
  40. Segment(K, J) → m
  41. Segment(Z, Y) → n
  42. Segment(C1, D1) → p
  43. Segment(T, S) → q
  44. Segment(W, V) → r
  45. Segment(Q, P) → s
  46. Segment(E, D) → t
  47. Point(Circle[N, 4]) → O
  48. Segment(N, O) → a_1
  49. Rotate(O, 120*°, N) → M
  50. Angle(O, N, M) → κ
  51. Segment(N, M) → b_1
  52. Point(Circle[B, 4]) → C
  53. Segment(B, C) → c_1
  54. Rotate(C, 150*°, B) → A
  55. Angle(C, B, A) → λ
  56. Segment(B, A) → d_1