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Interactive Triangle Angle Sum Theorem Demo

Interactive Triangle Angle Sum Theorem Demo
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2019-02-25 09:28
TriangleAngleGeometric Construction
In collections Triangle Theorems
This example demonstrates the Triangle Angle Sum Theorem through interactive manipulation, visually proving that the sum of interior angles in any triangle equals 180 degrees. Key math concepts include angle measurement, triangle geometry, and geometric transformations. Construction highlights GeoGebra commands like Rotate, Segment, and Polygon for dynamic visualization. Suitable for middle school and above students to explore geometric proofs and applications.

GeoGebra Commands & Parameters

  1. Rotate(B, (a * π / 180), A) → B'
  2. Segment(A, B) → f
  3. Ray(A, B') → g
  4. Point(g) → C
  5. Polygon(A, B, C) → t1, c, a_1, b
  6. Segment(B, C) → h
  7. Segment(C, A) → i
  8. Min({f, h, i}) → d
  9. Circle(A, (0.3 * d)) → e
  10. Circle(B, (0.3 * d)) → k
  11. Circle(C, (0.3 * d)) → p
  12. Angle(C, B, A) → β
  13. Intersect(e, f) → D,
  14. Intersect(k, h) → E,
  15. Intersect(p, i) → F,
  16. Rotate(D, If[0 < j ≤ 1, ((j * a) * π / 180), (a * π / 180)], A) → D'
  17. CircleSector(A, D, D') → q
  18. Rotate(E, If[1 < j ≤ 2, ((j - 1) * β), β], B) → E'
  19. CircleSector(B, E, E') → r
  20. Rotate(F, If[2 < j ≤ 3, ((j - 2) * (π - β - (a * π / 180))), π - β - (a * π / 180)], C) → F'
  21. CircleSector(C, F, F') → s
  22. Dilate(B, If[4 < j ≤ 5, 5 - j, 0], A) → B'_1
  23. Vector(B, B'_1) → u
  24. Translate(A, u) → A'
  25. Translate(B, u) → B'_2
  26. Translate(C, u) → C'
  27. Polygon(A', B'_2, C') → t1', c', a', b'_2
  28. Translate(B, u) → B'_3
  29. Translate(C, u) → C'_1
  30. Segment(B'_3, C'_1) → h'
  31. Translate(q, u) → q'
  32. Translate(s, u) → s'
  33. Translate(C, u) → C'_2
  34. Translate(A, u) → A'_1
  35. Segment(C'_2, A'_1) → i'
  36. Translate(r, u) → r'
  37. Midpoint(i) → G
  38. Rotate(A, If[5.5 < j ≤ 6.5, ((j - 5.5) * π), π], G) → A'_2
  39. Rotate(B, If[5.5 < j ≤ 6.5, ((j - 5.5) * π), π], G) → B'_4
  40. Rotate(C, If[5.5 < j ≤ 6.5, ((j - 5.5) * π), π], G) → C'_3
  41. Polygon(A'_2, B'_4, C'_3) → t1'_1, c'_3, a'_2, b'_4
  42. Segment(C'_3, B'_4) → l
  43. Segment(B'_4, A'_2) → m
  44. Segment(A'_2, C'_3) → n
  45. Rotate(s, If[5.5 < j ≤ 6.5, ((j - 5.5) * π), π], G) → s'_1
  46. Rotate(q, If[5.5 < j ≤ 6.5, ((j - 5.5) * π), π], G) → q'_1
  47. Rotate(r, If[5.5 < j ≤ 6.5, ((j - 5.5) * π), π], G) → r'_1
  48. Translate(A, u) → A'_3
  49. Translate(B, u) → B'_5
  50. Segment(A'_3, B'_5) → f'
  51. Rotate(D, If[9 < j ≤ 10, ((j - 9) * π), π], A) → D'_1
  52. CircleArc(A, D, D'_1) → t