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Inscribed Angle Theorem Demonstration

Inscribed Angle Theorem Demonstration
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2015-11-09 04:42
CircleAngleGeometric Construction
In collections Circles (Theorems)
This example demonstrates the Inscribed Angle Theorem: if two inscribed angles intercept the same arc, then they are equal. It involves core concepts like circle, inscribed angle, central angle, and arc. Construction highlights include using GeoGebra commands such as Circle, Point, CircleArc, Segment, Intersect, CircleSector, Dilate, Vector, Translate, Line, Angle, and Rotate, with objects like points A, B, C, D, O, P. Suitable for high school mathematics teaching to visually understand the theorem and its applications.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. CircleArc(A, C, D) → d
  5. CircleArc(A, D, C) → e
  6. Point(e) → E
  7. Point(e) → F
  8. Point(e) → J
  9. Point(e) → K
  10. Point(e) → M
  11. Segment(E, C) → a
  12. Segment(E, D) → b
  13. Segment(F, C) → f
  14. Segment(F, D) → g
  15. Segment(J, C) → n
  16. Segment(J, D) → p
  17. Segment(K, C) → q
  18. Segment(K, D) → r
  19. Segment(M, C) → a_1
  20. Segment(M, D) → b_1
  21. Circle(E, 1.5) → e_1
  22. Circle(F, 1.5) → f_1
  23. Circle(J, 1.5) → p_1
  24. Circle(K, 1.5) → q_1
  25. Circle(M, 1.5) → s_1
  26. Intersect(e_1, a, 1) → O
  27. Intersect(e_1, b, 1) → P
  28. Intersect(f_1, f, 1) → Q
  29. Intersect(f_1, g, 1) → R
  30. Intersect(p_1, n, 1) → A_1
  31. Intersect(p_1, p, 1) → B_1
  32. Intersect(q_1, q, 1) → C_1
  33. Intersect(q_1, r, 1) → D_1
  34. Intersect(s_1, a_1, 1) → G_1
  35. Intersect(s_1, b_1, 1) → H_1
  36. CircleSector(E, O, P) → c_2
  37. CircleSector(F, Q, R) → d_2
  38. CircleSector(J, A_1, B_1) → h_2
  39. CircleSector(K, C_1, D_1) → k_2
  40. CircleSector(M, G_1, H_1) → q_2
  41. Dilate(E, If[0 < o < 1, 1 - o, 0], F) → E'
  42. Vector(E, E') → u
  43. Translate(c_2, u) → s_2
  44. Line(E, g) → i_1
  45. Line(R, b) → j_1
  46. Line(F, j_1) → l_1
  47. Intersect(f_1, l_1, 2) → K_1
  48. Angle(R, F, K_1) → α
  49. Vector(F, J) → v
  50. Dilate(F, If[1.5 < o < 2.5, 2.5 - o, 0], J) → F'
  51. Vector(F, F') → w
  52. Translate(d_2, w) → h
  53. Angle(O, E, P) → β
  54. Angle(Q, F, R) → γ
  55. Line(J, g) → i
  56. Intersect(p_1, i, 2) → G
  57. Angle(B_1, J, G) → δ
  58. Angle(A_1, J, B_1) → ε
  59. Dilate(J, If[3 < o < 4, 4 - o, 0], K) → J'
  60. Vector(J, J') → j
  61. Translate(h_2, j) → k
  62. Line(K, p) → l
  63. Intersect(q_1, l) → H, I
  64. Angle(D_1, K, I) → ζ
  65. Angle(C_1, K, D_1) → η
  66. Dilate(K, If[4.5 < o < 5.5, 5.5 - o, 0], M) → K'
  67. Vector(K, K') → m
  68. Translate(k_2, m) → s
  69. Line(M, r) → t
  70. Intersect(s_1, t) → L, N
  71. Angle(H_1, M, N) → θ
  72. Angle(G_1, M, H_1) → ι
  73. Rotate(s_2, If[0 < o < 1, (o * (-α)), 0], E') → t_2
  74. Rotate(h, If[1.5 < o < 2.5, ((o - 1.5) * (-δ)), 0], F') → h'
  75. Rotate(k, If[3 < o < 4, ((o - 3) * (-ζ)), 0], J') → k'
  76. Rotate(s, If[4.5 < o < 5.5, ((o - 4.5) * (-θ)), 0], K') → s'