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Exterior Angles of a Quadrilateral

Exterior Angles of a Quadrilateral
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2017-06-15 07:47
PolygonAngle
In collections Congruence (CO) Cluster Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles
This example demonstrates a quick discovery activity for the exterior angles of a quadrilateral. Key mathematical concepts include the properties of exterior angles in a quadrilateral. Using GeoGebra commands such as Rotate, Angle, Ray, etc., the shape of the quadrilateral can be dynamically modified to observe changes in the exterior angles. Suitable for middle school and above students for geometric construction and exploration.

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