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Exterior Angle Theorem Demo by Kerry Gallagher

Exterior Angle Theorem Demo by Kerry Gallagher
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2017-05-01 02:26
TriangleAngleGeometric Construction
This example demonstrates the properties and theorem of exterior angles in triangles. It involves core concepts like the corollary to the Triangle Angle Sum Theorem, where an exterior angle equals the sum of the two non-adjacent interior angles. Construction uses commands such as Line, Slope, PointIn, Segment, Circle, Ray, Point, Intersect, Polygon, Dilate, Vector, Translate, Rotate. Suitable for middle school and above mathematics education to visually understand geometric theorems.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Slope(f) → a
  3. PointIn(c) → C
  4. Segment(A, C) → g
  5. Segment(C, B) → h
  6. Segment(B, A) → i
  7. Min(list1) → d
  8. Circle(A, (0.2 * d)) → e
  9. Circle(B, (0.2 * d)) → k
  10. Circle(C, (0.2 * d)) → p
  11. Ray(A, B) → j
  12. Ray(B, C) → l
  13. Ray(C, A) → m
  14. Point(j) → D
  15. Point(l) → E
  16. Point(m) → F
  17. Ray(B, D) → n
  18. Ray(C, E) → q
  19. Ray(A, F) → r
  20. Intersect(p, g, 1) → G
  21. Intersect(p, h, 1) → H
  22. Intersect(e, i, 1) → I
  23. Intersect(e, g, 1) → J
  24. CircleSector(A, I, J) → s
  25. CircleSector(C, G, H) → t
  26. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  27. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  28. Vector(A, A') → u
  29. Translate(s, u) → s'
  30. CircleArc(A, I, J) → d_1
  31. Distance(A, I) → v
  32. Rotate(t, If[1 < o ≤ 2, ((o - 1) * π), π], C) → t'
  33. CircleArc(C, G, H) → e_1
  34. Angle(G, C, H) → α
  35. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], B) → C'
  36. Vector(C, C') → u_1
  37. Translate(t', u_1) → t''
  38. Intersect(k, n) → K,
  39. Intersect(k, h) → L,
  40. CircleArc(B, K, L) → f_1