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Triangle Angle Sum Interactive Demonstration

Triangle Angle Sum Interactive Demonstration
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2012-11-13 17:36
TrianglePolygonAngleGeometric Construction
This GeoGebra example demonstrates the triangle angle sum theorem, illustrating that the sum of the three interior angles of any triangle is invariant at 180 degrees. The core mathematical concepts include Euclidean triangle geometry, interior angle relationships, angle measurement, and polygon construction. The figure is built using GeoGebra commands such as Polygon to form the triangle, Angle to label vertices α, β, and γ, Circle and Intersect to create intersection points, Segment and Midpoint for segments and midpoints, LineBisector for angle bisectors, Vector for directional elements, and If for conditional logic, with text objects tekst1 and tekst2 displaying angle values. It is suitable for middle school and high school mathematics instruction, supporting classroom demonstrations and student-centered exploration of triangle angle properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → mnogokut1, c, a, b
  2. Angle(A, B, C) → β
  3. Angle(C, A, B) → α
  4. Angle(A, C, B) → γ
  5. Circle(A, 2.0) → d
  6. Circle(B, 2.0) → e
  7. Circle(C, 2.0) → f
  8. Intersect(d, b) → D,
  9. Intersect(d, c) → E,
  10. Intersect(e, c) → F,
  11. Intersect(e, a) → G,
  12. Intersect(f, b) → H,
  13. Intersect(f, a) → I,
  14. Vector(A, C) → u
  15. If(t ≤ 1.0, Translate[A, t * u], Translate[A, u]) → A'
  16. If(t ≤ 1.0, Translate[D, t * u], Translate[D, u]) → D'
  17. If(t ≤ 1.0, Translate[E, t * u], Translate[E, u]) → E'
  18. Segment(A', D') → g
  19. Segment(A', E') → h
  20. Angle(D', A', E') → δ
  21. Vector(B, C) → v
  22. If(t ≤ 1.0, Translate[B, 0.0 * v], If[t > 1.0 ∧ t ≤ 2.0, Translate[B, (t - 1.0) * v], Translate[B, v]]) → B'
  23. If(t ≤ 1.0, Translate[G, 0.0 * v], If[t > 1.0 ∧ t ≤ 2.0, Translate[G, (t - 1.0) * v], Translate[G, v]]) → G'
  24. If(t ≤ 1.0, Translate[F, 0.0 * v], If[t > 1.0 ∧ t ≤ 2.0, Translate[F, (t - 1.0) * v], Translate[F, v]]) → F'
  25. Segment(G', B') → i
  26. Segment(F', B') → j
  27. Angle(F', B', G') → ε
  28. If(t ≤ 2.0, Rotate[I, 0.0*°, C], If[t > 2.0 ∧ t ≤ 3.0, Rotate[I, ((t - 2.0) * 180.0)°, C], Rotate[I, 180.0*°, C]]) → I'
  29. If(t ≤ 2.0, Rotate[H, 0.0*°, C], If[t > 2.0 ∧ t ≤ 3.0, Rotate[H, ((t - 2.0) * 180.0)°, C], Rotate[H, 180.0*°, C]]) → H'
  30. Segment(C, I') → l
  31. Angle(H', C, I') → ζ
  32. If(t ≤ 3.0, Text[""], If[t > 3.0 ∧ t < 4.0, Text["α + β + γ = ???"], Text["α + β + γ = 180°"]]) → tekst4
  33. Midpoint(b) → P_b
  34. Midpoint(c) → P_c
  35. Midpoint(a) → P_a
  36. If(γ < 90.0° ∧ α < 90.0° ∧ β < 90.0°, "šiljastokutan", If[γ ≟ 90.0° ∨ α ≟ 90.0° ∨ β ≟ 90.0°, "pravokutan", "tupokutan"]) → tekst6
  37. If((zaokr_a ≠ zaokr_b) ∧ (zaokr_a ≠ zaokr_c) ∧ (zaokr_b ≠ zaokr_c), "raznostraničan", If[zaokr_a ≟ zaokr_b ∧ zaokr_a ≟ zaokr_c ∧ zaokr_b ≟ zaokr_c, "jednakostraničan", "jednakokračan"]) → tekst7
  38. If(tekst7 ≟ "raznostraničan", Text["a = " + a], If[tekst7 ≟ "jednakokračan" ∧ zaokr_b ≟ zaokr_c, Text["a = " + a], If[tekst7 ≟ "jednakokračan" ∧ (zaokr_b ≟ zaokr_a ∨ zaokr_c ≟ zaokr_a), Text["b = " + a], Text["a = " + a]]]) → tekst8
  39. If(tekst7 ≟ "raznostraničan", Text["b = " + b], If[tekst7 ≟ "jednakokračan" ∧ zaokr_a ≟ zaokr_c, Text["a = " + b], If[tekst7 ≟ "jednakokračan" ∧ (zaokr_a ≟ zaokr_b ∨ zaokr_c ≟ zaokr_b), Text["b = " + b], Text["a = " + b]]]) → tekst9
  40. If(tekst7 ≟ "raznostraničan", Text["c = " + c], If[tekst7 ≟ "jednakokračan" ∧ zaokr_a ≟ zaokr_b, Text["a = " + c], If[tekst7 ≟ "jednakokračan" ∧ (zaokr_a ≟ zaokr_c ∨ zaokr_b ≟ zaokr_c), Text["b = " + c], Text["a = " + c]]]) → tekst10
  41. LineBisector(c) → s_c
  42. LineBisector(a) → s_a
  43. LineBisector(b) → s_b
  44. Angle(s_c, c) → η
  45. Angle(s_b, b) → θ
  46. Angle(s_a, a) → ι