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Triangle Solving Examples

Triangle Solving Examples
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2019-04-15 10:07
TriangleVectorTrigonometryCoordinate GeometryGeometric Construction
In collections MA440
This example demonstrates solving triangles using various given conditions (SSS, SAS, ASA, AAS). It involves core mathematical concepts like triangle construction, angle measurement, side length calculation, trigonometric function application, similarity transformation, and 3D vectors. Construction highlights include commands like Random, If, Point, Segment, Circle, Intersect, Angle, Rotate, Ray, and objects such as F7, F6, E2, A11, etc., used to randomly generate triangles and showcase different solving methods. Suitable for high school mathematics education to understand the diversity and practical applications of triangle solving techniques.

GeoGebra Commands & Parameters

  1. Random(1, 10) → E2
  2. Random(1, 10) → E4
  3. Random(1, 7) → randNum
  4. If(randNum ≟ 4, true, false) → SAS
  5. If(randNum ≟ 3, true, false) → AAS
  6. If(randNum ≟ 2, true, false) → ASA
  7. If(randNum ≟ 1, true, false) → SSS
  8. Random(1, 178) → D5
  9. Random(1, 179 - D5) → D6
  10. Random(1, 178) → C5
  11. Random(1, 179 - C5) → C7
  12. Random(1, 10) → B3
  13. Random(1, 10) → B2
  14. Random(B2 + B3 - 1, abs(B2 - B3) + 1) → B4
  15. Random(1, 178) → E6
  16. If(H11 ≟ 180, F12, F11) → E7
  17. Random(10, 110) → F5
  18. Random(1, 10) → D3
  19. Random(1, 10) → C3
  20. Random(3, 10) → F2
  21. Random(5, 10) → F3
  22. If(¬Defined[C17], 0, If[C17 < 0, 0, 1]) → H17
  23. If(H12 ≟ 180, D12, D11) → E5
  24. Point(Circle[A, B2]) → B
  25. Segment(A, B) → f
  26. Circle(A, B3) → c
  27. Circle(B, B4) → d
  28. Intersect(c, d, 1) → C
  29. Segment(A, C) → g
  30. Segment(B, C) → h
  31. Angle(B, A, C) → α
  32. Angle(C, B, A) → β
  33. Angle(A, C, B) → γ
  34. Point(Circle[D, C3]) → E
  35. Segment(D, E) → i
  36. Rotate(D, (-(C5°)), E) → D'
  37. Angle(D', E, D) → δ
  38. Rotate(E, C7°, D) → E'
  39. Angle(E, D, E') → ε
  40. Ray(D, E') → j
  41. Ray(E, D') → k
  42. Intersect(j, k) → F
  43. Segment(D, F) → l
  44. Segment(F, E) → m
  45. Angle(D, F, E) → ζ
  46. Point(Circle[G, D3]) → H
  47. Segment(G, H) → n
  48. Rotate(H, D5°, G) → H'
  49. Angle(H, G, H') → η
  50. Ray(G, H') → p
  51. Point(p) → I
  52. Rotate(G, D6°, I) → G'
  53. Angle(G, I, G') → θ
  54. Ray(I, G') → q
  55. Circle(G, D4) → e
  56. Intersect(e, p, 1) → J
  57. Segment(G, J) → r
  58. Segment(H, J) → s
  59. Angle(J, H, G) → ι
  60. Angle(G, J, H) → κ
  61. Point(Circle[K, E2]) → L
  62. Segment(K, L) → t
  63. Rotate(L, E6°, K) → L'
  64. Angle(L, K, L') → λ
  65. Ray(K, L') → a
  66. Circle(K, E4) → c_1
  67. Intersect(c_1, a, 1) → M
  68. Segment(K, M) → b
  69. Segment(M, L) → f_1
  70. Angle(K, M, L) → μ
  71. Angle(M, L, K) → ν
  72. If(randNum > 4, true, false) → SSA
  73. Point(Circle[N, F2]) → O
  74. Segment(N, O) → g_1
  75. Point(Circle[N, F3]) → P
  76. Segment(N, P) → h_1
  77. Rotate(N, (-(F5°)), P) → N'
  78. Angle(N', P, N) → ξ
  79. If(C18 < 0, 0, If[A18 ≟ B18, 0, If[Defined[C18], 1, 0]]) → H18
  80. Ray(P, N') → i_1
  81. If(SSAnumTri ≟ 0, true, false) → SSAnoTri
  82. If(SSA ≟ true, If[H17 ≟ 1, true, false], false) → SSA1
  83. If(SSA ≟ true, If[H18 ≟ 1, true, false], false) → SSA2
  84. Circle(P, G4) → d_1
  85. Intersect(d_1, i_1, 1) → Q
  86. Segment(P, Q) → j_1
  87. Segment(N, Q) → k_1
  88. Angle(N, Q, P) → ο
  89. Angle(P, N, Q) → ρ
  90. Circle(P, H4) → e_1
  91. Intersect(e_1, j_1, 1) → R
  92. Segment(N, R) → l_1
  93. Segment(R, P) → m_1
  94. Segment(N, P) → n_1
  95. Angle(P, N, R) → σ
  96. Angle(N, R, P) → τ
  97. If(SSS ≟ true, B2, If[ASA ≟ true, If[showSolution ≟ true, C2, NaN], If[AAS ≟ true, If[showSolution ≟ true, D2, NaN], If[SAS ≟ true, E2, F2]]]) → smallA
  98. If(SSS ≟ true, B4, If[ASA ≟ true, If[showSolution ≟ true, C4, NaN], If[AAS ≟ true, If[showSolution ≟ true, D4, NaN], If[SAS ≟ true, E4, If[showSolution ≟ true, G4, NaN]]]]) → smallC
  99. If(SSS ≟ true, B3, If[ASA ≟ true, C3, If[AAS ≟ true, D3, If[SAS ≟ true, If[showSolution ≟ true, E3, NaN], G3]]]) → smallB
  100. If(SSS ≟ true, If[showSolution ≟ true, B6, NaN], If[ASA ≟ true, If[showSolution ≟ true, C6, NaN], If[AAS ≟ true, D6, If[SAS ≟ true, E6, If[showSolution ≟ true, G6, NaN]]]]) → bigB
  101. If(SSS ≟ true, If[showSolution ≟ true, B7, NaN], If[ASA ≟ true, C7, If[AAS ≟ true, If[showSolution ≟ true, D7, NaN], If[SAS ≟ true, If[showSolution ≟ true, E2, NaN], If[showSolution ≟ true, G7, NaN]]]]) → bigC
  102. If(SSS ≟ true, If[showSolution ≟ true, B5, NaN], If[ASA ≟ true, C5, If[AAS ≟ true, D5, If[SAS ≟ true, If[showSolution ≟ true, E5, NaN], F5]]]) → bigA
  103. If(showSolution ≟ true, ((smallA * smallB) * sin((bigC * π / 180)) / 2), NaN) → area