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Alternate Exterior Angles Theorem Demo

Alternate Exterior Angles Theorem Demo
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2018-10-22 10:42
AngleTransformationGeometric Construction
This example dynamically demonstrates the proof that alternate exterior angles are congruent when a transversal intersects two parallel lines. It involves core concepts like parallel lines, transversal, alternate exterior angles, and geometric transformations. Constructed using GeoGebra commands and objects such as Point, Rotate, Angle, Line, Circle, Intersect, CircleSector, Dilate, Vector, Midpoint, Segment, Ray, CircleArc. Suitable for high school mathematics students to learn and understand geometric theorems.

GeoGebra Commands & Parameters

  1. Point(a) → B
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Line(A, B') → b
  5. Circle(A, 1) → e
  6. Intersect(b, d) → C
  7. Circle(C, 1) → f
  8. Intersect(e, a) → D, E
  9. Intersect(e, b) → F, G
  10. Intersect(f, b) → H, I
  11. Intersect(f, d) → J, K
  12. CircleSector(C, J, H) → k
  13. CircleSector(C, H, K) → p
  14. CircleSector(A, F, E) → t
  15. Dilate(A, If[0 < i < 1, 1 - i], C) → A'
  16. Vector(A, A') → u
  17. Vector(A, C) → v
  18. Midpoint(C, A) → L
  19. Rotate(A, (((-i) * 180))°, L) → A'_1
  20. Segment(L, A'_1) → g
  21. Segment(C, L) → n
  22. Segment(L, A) → s
  23. Point(b) → M
  24. Point(b) → N
  25. Ray(C, M) → a_1
  26. Ray(A, N) → b_1
  27. Rotate(E, (((-i) * 180))°, L) → E'
  28. Ray(A'_1, E') → d_1
  29. Circle(A'_1, Distance[L, A'_1]) → e_1
  30. Intersect(e_1, d_1, 1) → O
  31. Rotate(A, ((i * 180))°, L) → A'_2
  32. Rotate(D, ((i * 180))°, L) → D'
  33. Circle(A'_2, L) → k_1
  34. Ray(A'_2, D') → i_1
  35. Intersect(k_1, i_1) → P,
  36. Segment(A'_2, P) → j_1
  37. Intersect(e, b, 1) → Q
  38. Intersect(f, n, 1) → R
  39. CircleSector(A, Q, E) → c_1
  40. Rotate(c_1, (((-i) * 180))°, L) → q
  41. Rotate(Q, (((-i) * 180))°, L) → Q'
  42. Circle(A, g) → g_1
  43. Intersect(g_1, b_1, 1) → S
  44. Intersect(g_1, a, 2) → T
  45. Segment(A, S) → h_1
  46. Rotate(A, (((-i) * 180))°, L) → A'_3
  47. Rotate(S, (((-i) * 180))°, L) → S'
  48. Segment(A'_3, S') → l_1
  49. Segment(A, T) → m_1
  50. Rotate(A, (((-i) * 180))°, L) → A'_4
  51. Rotate(T, (((-i) * 180))°, L) → T'
  52. Segment(A'_4, T') → n_1
  53. CircleArc(A, Q, E) → p_1
  54. Intersect(e_1, a, 1) → U
  55. Segment(A, U) → q_1
  56. Intersect(a, q_1) → V
  57. Intersect(a, q_1) → W
  58. Intersect(e, a, 1) → Z
  59. CircleSector(A, Z, Q) → r
  60. Rotate(A, ((i * 180))°, L) → A'_5
  61. Rotate(r, ((i * 180))°, L) → r'
  62. Rotate(A, ((i * 180))°, L) → A'_6
  63. Rotate(S, ((i * 180))°, L) → S'_1
  64. Segment(A'_6, S'_1) → h
  65. Segment(L, A'_5) → r_1
  66. CircleArc(A, Z, Q) → f_1