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Solving Right Triangles Quiz

Solving Right Triangles Quiz
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2014-11-11 11:57
TriangleTrigonometryGeometric Construction
This example demonstrates solving right triangle problems using the Pythagorean theorem and trigonometric functions. It involves constructing geometric figures with commands like Random, Intersect, Circle, Segment, If, Angle, Rotate, Line, OrthogonalLine. Suitable for high school geometry instruction and construction practice.

GeoGebra Commands & Parameters

  1. Random(40, 75) → d_5
  2. Random(4, 10) → b_5
  3. Random(3, 7) → b_4
  4. Random(15, 60) → d_4
  5. Random(3, 8) → b_1
  6. Random(3, 10) → c_1
  7. Intersect(v_2, v'_2) → F
  8. Circle(D, If[c_1 ≟ b_1, c_1 + 2, If[c_1 > b_1, c_1, b_1]]) → circle_2
  9. Intersect(circle_2, v_2, 2) → E
  10. Segment(E, F) → d
  11. Segment(D, E) → f
  12. Segment(F, D) → e
  13. Random(2, 10) → a_1
  14. Intersect(xAxis, yAxis) → C
  15. Segment(C, A) → b
  16. Segment(B, C) → a
  17. Intersect(v_3, xAxis) → H
  18. Segment(A, B) → c
  19. Random(1, 5) → version
  20. If(abs(AB - c) ≤ 0.05, 1, 0) → e_1
  21. If(Angle_ B ≟ (round((180 * atan(b / a) / 3.141592653589793)))°, 1, 0) → g_1
  22. If(Angle_ A ≟ (round((180 * atan(a / b) / 3.141592653589793)))°, 1, 0) → f_1
  23. Angle(A, C, B) → C_1
  24. If(e_1 + f_1 + g_1 ≟ 3, 1, 0) → h_1
  25. Angle(D, F, E) → F_2
  26. If(abs(EF - d) ≤ 0.05, 1, 0) → e_2
  27. If(Angle_ E ≟ (round((180 * asin(e / f) / 3.141592653589793)))°, 1, 0) → g_2
  28. If(Angle_ D ≟ (round((180 * acos(e / f) / 3.141592653589793)))°, 1, 0) → f_2
  29. If(e_2 + f_2 + g_2 ≟ 3, 1, 0) → h_2
  30. Random(15, 75) → d_1
  31. Rotate(G, d_1°, H) → A'_3
  32. Angle(G, H, A'_3) → H_3
  33. Line(A'_3, H) → perpto_3
  34. OrthogonalLine(G, perpto_3) → perp_3
  35. Intersect(perp_3, perpto_3) → J
  36. Segment(G, H) → j
  37. Segment(H, J) → g
  38. Segment(J, G) → h
  39. Angle(H, J, G) → J_3
  40. If(abs(HJ - g) ≤ 0.05, 1, 0) → f_3
  41. If(Angle_ G ≟ 90° - d_1°, 1, 0) → e_3
  42. If(abs(GJ - h) ≤ 0.05, 1, 0) → g_3
  43. If(e_3 + f_3 + g_3 ≟ 3, 1, 0) → h_3
  44. Intersect(yAxis, xAxis) → K
  45. Segment(N, K) → m
  46. Rotate(N, (-(d_4°)), K) → C'_4
  47. Angle(C'_4, K, N) → K_4
  48. OrthogonalLine(N, m) → perp_4
  49. Intersect(Line[K, C'_4], perp_4) → M
  50. Segment(N, M) → k
  51. Segment(M, K) → n
  52. Angle(K, N, M) → N_4
  53. If(Angle_ M ≟ 90° - d_4°, 1, 0) → e_4
  54. If(abs(MN - k) ≤ 0.05, 1, 0) → f_4
  55. If(abs(KM - n) ≤ 0.05, 1, 0) → g_4
  56. If(e_4 + f_4 + g_4 ≟ 3, 1, 0) → h_4
  57. Rotate(R, 90° - d_5°, O) → C'_5
  58. Angle(R, O, C'_5) → O_1
  59. Line(O, C'_5) → perpintersect_5
  60. Segment(O, R) → p
  61. OrthogonalLine(R, p) → perp_5
  62. Intersect(perpintersect_5, perp_5) → P
  63. Angle(O, P, R) → P_5
  64. Angle(P, R, O) → R_5
  65. Segment(O, P) → r
  66. Segment(P, R) → o
  67. If(Angle_ O ≟ 90° - d_5°, 1, 0) → e_5
  68. If(abs(PR - o) ≤ 0.05, 1, 0) → f_5
  69. If(abs(OP - r) ≤ 0.05, 1, 0) → g_5
  70. If(e_5 + f_5 + g_5 ≟ 3, 1, 0) → h_5
  71. Angle(C, B, A) → B_1
  72. Angle(B, A, C) → A_1
  73. Angle(E, D, F) → D_2
  74. Angle(F, E, D) → E_2
  75. Angle(J, G, H) → G_3
  76. Angle(N, M, K) → M_4
  77. Angle(R, O, P) → O_5

AI Drawing Prompt Reference

Draw a right triangle with one leg length and the hypotenuse length randomly generated. Use sine and cosine functions to calculate the degree of the other acute angle and ensure the angles and side lengths meet the properties of a right triangle. Then, construct a rotated triangle with one right angle and a randomly generated side length. Finally, construct a line segment perpendicular to a given line, ensuring its length meets the given conditions.
The prompt above was compiled from the original drawing commands and is for reference only.