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Quadrilateral Exterior Angles Dynamic Exploration

Quadrilateral Exterior Angles Dynamic Exploration
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2019-07-17 22:21
PolygonAngleTransformationGeometric Construction
This GeoGebra example demonstrates the theorem that the sum of exterior angles of a quadrilateral equals 360 degrees. Key concepts include polygon exterior angles, angle measurement, and geometric invariance. Construction utilizes commands like Rotate, Angle, Ray, Segment, and Polygon to create a dynamic, modifiable figure. Ideal for middle school geometry students or teachers for interactive classroom demonstrations to visualize the exterior angle sum theorem.

GeoGebra Commands & Parameters

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Ray(B, A') → f
  4. Segment(B, A) → g
  5. Point(f) → C
  6. Angle(B, C, A) → β
  7. Rotate(B, γ, C) → B'
  8. Angle(B, C, B') → δ
  9. Ray(C, B') → h
  10. Point(h) → D
  11. Ray(D, A) → i
  12. Segment(A, B) → j
  13. Segment(B, C) → k
  14. Segment(C, D) → l
  15. Segment(D, A) → m
  16. Min({j, k, l, m}) → b
  17. Ray(A, B) → n
  18. Ray(B, C) → p
  19. Circle(B, (0.25 * b)) → c
  20. Intersect(c, n, 2) → E
  21. Intersect(c, p, 1) → F
  22. Circle(C, (0.25 * b)) → d
  23. Circle(D, (0.25 * b)) → e
  24. Circle(A, (0.25 * b)) → q
  25. Intersect(d, h, 1) → G
  26. Intersect(d, p, 2) → H
  27. Intersect(e, i, 1) → I
  28. Intersect(e, h, 2) → J
  29. Intersect(q, n, 1) → K
  30. Intersect(q, i, 2) → L
  31. CircleSector(B, F, E) → r
  32. CircleSector(C, G, H) → s
  33. CircleSector(D, I, J) → t
  34. CircleSector(A, K, L) → c_1
  35. Angle(C, D, A) → ε
  36. Line(B, A) → f_1
  37. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], B) → A'_1
  38. Vector(A, A'_1) → v
  39. Translate(c_1, v) → d_1
  40. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], C) → B'_1
  41. Vector(B, B'_1) → w
  42. Translate(d_1, w) → e_1
  43. Translate(r, w) → r'
  44. Dilate(C, If[2 < u ≤ 3, 3 - u, 0], D) → C'
  45. Vector(C, C') → u_1
  46. Translate(r', u_1) → r''
  47. Translate(s, u_1) → s'
  48. Translate(e_1, u_1) → g_1
  49. Polygon(B, A, D, C) → poly1, b_1, a_1, d_2, c_2