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P3 Triangle Construction 3 (Grid/Check Answers/One Side Fixed/Advanced)

P3 Triangle Construction 3 (Grid/Check Answers/One Side Fixed/Advanced)
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2020-02-26 18:54
TriangleCoordinate GeometryGeometric Construction
This example demonstrates triangle construction in a grid environment with the ability to check answers, where one side is fixed, suitable for advanced learners. Core math concepts include triangle construction, side lengths, angles, and vector operations. Construction highlights include commands like IndexOf, Segment, Sequence, RandomElement, Vector, If, and objects like ListTriType, TriType, etc. Ideal for high school mathematics teaching, geometry practice, and concept deepening.

GeoGebra Commands & Parameters

  1. IndexOf(SelectedElement[ListTriType], ListTriType) → TriType
  2. Segment(Blue1a, Blue1b) → SegBlue1
  3. Segment(Blue2a, Blue2b) → SegBlue2
  4. Sequence(Sequence[(s, t), s, 0, 25], t, -5, 13) → ListDots
  5. RandomElement({4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}) → Redax12
  6. RandomElement({-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}) → Reday12
  7. RandomElement({4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}) → Redbx12
  8. RandomElement({-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}) → Redby12
  9. RandomElement({4, 5, 6, 7, 8, 9}) → Reday3
  10. RandomElement({4, 5, 6, 7, 8, 9}) → Redby3
  11. RandomElement({9, 10, 11, 12, 13, 14, 15, 16, 17}) → Redax4
  12. RandomElement({4, 5, 6}) → Reday4
  13. Vector((1, 0)) → VecE
  14. Vector((0, 1)) → VecN
  15. Vector((0, -1)) → VecS
  16. Vector((-1, 0)) → VecW
  17. Vector((1, 1)) → VecNE
  18. Vector((1, -1)) → VecSE
  19. Vector((-1, 1)) → VecNW
  20. Vector((-1, -1)) → VecSW
  21. RandomElement({1, 2, 3, 4}) → RanLength
  22. RandomElement({8, 9, 10, 11, 12, 13, 14, 15}) → Redax3
  23. If(TriType ≟ 1 ∨ TriType ≟ 2, Redax12, TriType ≟ 3, Redax3, Redax4) → Redax
  24. If(TriType ≟ 1 ∨ TriType ≟ 2, Reday12, TriType ≟ 3, Reday3, Reday4) → Reday
  25. RandomElement({9, 10, 11, 12, 13, 14}) → Redbx3
  26. If(TriType ≟ 1 ∨ TriType ≟ 2, Redbx12, TriType ≟ 3, Redbx3, Redbx4) → Redbx0
  27. If(TriType ≟ 1 ∨ TriType ≟ 2, Redby12, TriType ≟ 3, Redby3, Redby4) → Redby
  28. If(Redax ≟ Redbx0 ∧ Reday ≟ Redby, Redbx0 + 1, Redbx0) → Redbx
  29. Segment(Reda, Redb) → SegRed

AI Drawing Prompt Reference

Draw a triangle construction exercise on a grid background. Start with a fixed red segment whose endpoints are randomly chosen integer grid points, ensuring they are distinct. Then, based on a randomly selected triangle type (such as equilateral, isosceles, or scalene), determine the third vertex's coordinates to satisfy the corresponding side length or angle conditions. Connect this third vertex to both endpoints of the red segment with blue segments to complete the triangle. The grid consists of evenly spaced dots for coordinate checking. This figure is intended for advanced geometry practice, focusing on triangle construction, side lengths, and vector directions.
The prompt above was compiled from the original drawing commands and is for reference only.