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Triangle Angles Game

Triangle Angles Game
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2012-12-02 21:56
TriangleAngleGeometric Construction
In collections Properties of Polygons
This is an interactive game for practicing the sum of interior and exterior angles of a triangle. Key mathematical concepts include the interior and exterior angles of a triangle. Using GeoGebra commands such as Angle, Polygon, and Line, the game dynamically demonstrates the angles of a triangle. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. If(rndNum ≟ 1, true, false) → AlfaBeta
  2. If(rndNum ≟ 2, true, false) → AlfaGama
  3. If(rndNum ≟ 3, true, false) → BetaGama
  4. Angle(C, A, B) → α
  5. Angle(C, B, A) → β
  6. Polygon(A_1, B_1, C_1, D_1) → mnogokut1, a_1, b_1, c_1, d_1
  7. Polygon(A, B, C) → mnogokut2, c, a_2, b
  8. Line(A, B) → d
  9. Rotate(C, round(180° - α), A) → C'
  10. Angle(C, A, C') → α'
  11. Line(C, B) → e
  12. Rotate(A, 180° - β, B) → A'
  13. Angle(A, B, A') → β'
  14. Line(A, C) → f
  15. Angle(A, C, B) → γ
  16. Rotate(B, round(180° - γ), C) → B'
  17. Angle(B, C, B') → γ'
  18. If(rndNum ≟ 4, true, false) → Alfa'Beta'
  19. If(rndNum ≟ 5, true, false) → Alfa'Gama'
  20. If(rndNum ≟ 6, true, false) → Beta'Gama'
  21. If(rndNum ≟ 7, true, false) → AlfaBeta'
  22. If(rndNum ≟ 8, true, false) → AlfaGama'
  23. If(rndNum ≟ 9, true, false) → BetaAlfa'
  24. If(rndNum ≟ 10, true, false) → BetaGama'
  25. If(rndNum ≟ 11, true, false) → GamaAlfa'
  26. If(rndNum ≟ 12, true, false) → GamaBeta'
  27. If(AlfaBeta ≟ true, "γ", If[AlfaGama ≟ true, "β", If[BetaGama ≟ true, "α", ""]]) → tekst1A
  28. Textfield(odgovor1A) → txtPolje1A
  29. If(AlfaBeta ≟ true, "γ'", If[AlfaGama ≟ true, "β'", If[BetaGama ≟ true, "α'", ""]]) → tekst1B
  30. Textfield(odgovor1B) → txtPolje1B
  31. If(AlfaBeta ≟ true, brojKutGama', If[AlfaGama ≟ true, brojKutBeta', If[BetaGama ≟ true, brojKutAlfa', 0*°]]) → zaokruzeniKut1B
  32. If(AlfaBeta ≟ true, brojKutGama, If[AlfaGama ≟ true, brojKutBeta, If[BetaGama ≟ true, brojKutAlfa, 0*°]]) → zaokruzeniKut1A
  33. If(abs(zaokruzeniKut1A - odgovor1A°) ≟ 0 ∧ abs(zaokruzeniKut1B - odgovor1B°) ≟ 0, "BRAVO! Točno!", If[abs(zaokruzeniKut1A - odgovor1A°) ≟ 0 ∧ (abs(zaokruzeniKut1B - odgovor1B°) ≠ 0), "Netočna veličina drugog kuta!", If[(abs(zaokruzeniKut1A - odgovor1A°) ≠ 0) ∧ abs(zaokruzeniKut1B - odgovor1B°) ≟ 0, "Netočna veličina prvog kuta!", "Nažalost, netočne veličine kutova!"]]) → provjera1
  34. If(Alfa'Beta' ≟ true, brojKutGama, If[Alfa'Gama' ≟ true, brojKutBeta, If[Beta'Gama' ≟ true, brojKutAlfa, 0*°]]) → zaokruzeniKut2A
  35. If(Alfa'Beta' ≟ true, brojKutGama', If[Alfa'Gama' ≟ true, brojKutBeta', If[Beta'Gama' ≟ true, brojKutAlfa', 0*°]]) → zaokruzeniKut2B
  36. If(Alfa'Beta' ≟ true, "γ", If[Alfa'Gama' ≟ true, "β", If[Beta'Gama' ≟ true, "α", ""]]) → tekst2A
  37. Textfield(odgovor2A) → txtPolje2A
  38. If(Alfa'Beta' ≟ true, "γ'", If[Alfa'Gama' ≟ true, "β'", If[Beta'Gama' ≟ true, "α'", ""]]) → tekst2B
  39. Textfield(odgovor2B) → txtPolje2B
  40. If(abs(zaokruzeniKut2A - odgovor2A°) ≟ 0 ∧ abs(zaokruzeniKut2B - odgovor2B°) ≟ 0, "BRAVO! Točno!", If[abs(zaokruzeniKut2A - odgovor2A°) ≟ 0 ∧ (abs(zaokruzeniKut2B - odgovor2B°) ≠ 0), "Netočna veličina drugog kuta!", If[(abs(zaokruzeniKut2A - odgovor2A°) ≠ 0) ∧ abs(zaokruzeniKut2B - odgovor2B°) ≟ 0, "Netočna veličina prvog kuta!", "Nažalost, netočne veličine kutova!"]]) → provjera2
  41. If(AlfaBeta' ≟ true, brojKutGama, If[AlfaGama' ≟ true, brojKutBeta, If[BetaAlfa' ≟ true, brojKutGama, If[BetaGama' ≟ true, brojKutAlfa, If[GamaAlfa' ≟ true, brojKutBeta, If[GamaBeta', brojKutAlfa, 0*°]]]]]) → zaokruzeniKut3A
  42. If(AlfaBeta' ≟ true, brojKutGama', If[AlfaGama' ≟ true, brojKutBeta', If[BetaAlfa' ≟ true, brojKutGama', If[BetaGama' ≟ true, brojKutAlfa', If[GamaAlfa' ≟ true, brojKutBeta', If[GamaBeta', brojKutAlfa', 0*°]]]]]) → zaokruzeniKut3B
  43. If(AlfaBeta' ≟ true, "γ", If[AlfaGama' ≟ true, "β", If[BetaAlfa' ≟ true, "γ", If[BetaGama' ≟ true, "α", If[GamaAlfa' ≟ true, "β", If[GamaBeta', "α", ""]]]]]) → tekst3A
  44. Textfield(odgovor3A) → txtPolje3A
  45. If(AlfaBeta' ≟ true, "γ'", If[AlfaGama' ≟ true, "β'", If[BetaAlfa' ≟ true, "γ'", If[BetaGama' ≟ true, "α'", If[GamaAlfa' ≟ true, "β'", If[GamaBeta', "α'", ""]]]]]) → tekst3B
  46. Textfield(odgovor3B) → txtPolje3B
  47. If(abs(zaokruzeniKut3A - odgovor3A°) ≟ 0 ∧ abs(zaokruzeniKut3B - odgovor3B°) ≟ 0, "BRAVO! Točno!", If[abs(zaokruzeniKut3A - odgovor3A°) ≟ 0 ∧ (abs(zaokruzeniKut3B - odgovor3B°) ≠ 0), "Netočna veličina drugog kuta!", If[(abs(zaokruzeniKut3A - odgovor3A°) ≠ 0) ∧ abs(zaokruzeniKut3B - odgovor3B°) ≟ 0, "Netočna veličina prvog kuta!", "Nažalost, netočne veličine kutova!"]]) → provjera3
  48. AngularBisector(B, C, B') → h
  49. AngularBisector(A, B, A') → g
  50. AngularBisector(C, A, C') → i
  51. Point(i) → D
  52. Point(g) → E
  53. Point(h) → F
  54. AngularBisector(C, A, B) → j
  55. Point(j) → G
  56. AngularBisector(C, B, A) → k
  57. Point(k) → H
  58. AngularBisector(A, C, B) → l
  59. Point(l) → I
  60. Angle(C, B, A) → β_p
  61. Angle(A, B, A') → β'_p
  62. Angle(A, C, B) → γ_p
  63. Angle(B, C, B') → γ'_p
  64. Angle(C, A, C') → α'_p
  65. Angle(C, A, B) → α_p

AI Drawing Prompt Reference

Draw a triangle and dynamically display its interior and exterior angles. First, draw the triangle and label its three interior angles α, β, γ, calculating their measures. Then, rotate each vertex around the midpoint of the opposite side by 180° to get new vertices C', A', B', and label the resulting interior angles α', β', γ'. Finally, draw the angle bisectors to demonstrate their properties.
The prompt above was compiled from the original drawing commands and is for reference only.