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Addition Postulate Explore

Addition Postulate Explore
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2014-10-15 15:47
TriangleAngleFunctionTrigonometryGeometric Construction
In collections Addition Postulate
This example helps visualize the concept of segment addition and angle addition. It involves core mathematical concepts such as line segment addition, angle addition, and basic trigonometric functions. Construction uses GeoGebra commands like Random, Rotate, CircleArc, Point, Angle, and Segment. Suitable for middle or high school mathematics to intuitively understand geometric and trigonometric principles.

GeoGebra Commands & Parameters

  1. Random(60, 270) → a
  2. Rotate(B, a°, A) → D
  3. CircleArc(A, B, D) → c
  4. Point(c) → C
  5. Angle(B, A, D) → α
  6. Angle(B, A, C) → β
  7. Angle(C, A, D) → γ
  8. Segment(A, C) → b
  9. Random(60, 270) → a_1
  10. Rotate(B_2, a_1°, A_2) → D_2
  11. CircleArc(A_2, B_2, D_2) → c_1
  12. Point(c_1) → C_2
  13. Angle(B_2, A_2, D_2) → α_1
  14. Angle(B_2, A_2, C_2) → β_1
  15. Angle(C_2, A_2, D_2) → γ_1
  16. Segment(A_2, C_2) → b_1
  17. Random(60, 270) → a_2
  18. Rotate(B_3, a_2°, A_3) → D_3
  19. CircleArc(A_3, B_3, D_3) → c_2
  20. Angle(B_3, A_3, D_3) → α_2
  21. Random(60, 270) → a_3
  22. Rotate(B_4, a_3°, A_4) → D_4
  23. CircleArc(A_4, B_4, D_4) → c_3
  24. Point(c_3) → C_3
  25. Angle(B_4, A_4, D_4) → α_3
  26. Angle(B_4, A_4, C_3) → β_2
  27. Angle(C_3, A_4, D_4) → γ_2
  28. Segment(A_4, C_3) → b_2
  29. Random(5, 20) → d
  30. Point(Circle[E_1, abs(d)]) → F_1
  31. Segment(E_1, F_1) → e
  32. Random(d + 5, d + 20) → f
  33. Point(Circle[G_1, abs(f)]) → H_1
  34. Segment(G_1, H_1) → h
  35. Point(Circle[J_1, abs(g)]) → K_1
  36. Segment(J_1, K_1) → i
  37. CircleArc(A, B, C) → k
  38. CircleArc(A, C, D) → p
  39. Random(5, 20) → d_1
  40. Random(5, 20) → d_2
  41. Random(d_2 + 5, d_2 + 20) → f_1
  42. Random(5, 20) → d_3
  43. Random(d_3 + 5, d_3 + 20) → f_2

AI Drawing Prompt Reference

Draw a geometric diagram to illustrate the concept of segment and angle addition. Include three rotating triangles, each with two segments and three angles, represented by arcs and connecting vertices. Start with the first triangle, then rotate the second and third triangles by random angles. Finally, add two randomly lengthed segments and circles to demonstrate basic trigonometric functions and geometric constructions.
The prompt above was compiled from the original drawing commands and is for reference only.