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P3 Moving Triangle: Dynamic Geometry Exploration

P3 Moving Triangle: Dynamic Geometry Exploration
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2020-11-07 12:28
TriangleTransformationGeometric ConstructionSlider AnimationLocus
① This example demonstrates a movable triangle in a dynamic geometry environment, allowing users to drag vertices or use sliders to observe changes in shape and position. ② Core mathematical concepts include triangle properties, medians, special points (e.g., centroid, orthocenter), and stochastic point generation, while integrating quadrilaterals and parabolic elements. ③ Construction highlights: using GeoGebra commands such as Sequence, If, Polygon, Segment, OrthogonalLine, Point, Midpoint, Circle, and Intersect, the construction builds multiple triangles (Tri1 to Tri4) with auxiliary lines and points, plus display toggles (ShowChi, ShowEng, etc.) and grid options (ShowIsoGrid, ShowSqGrid). ④ Suitable for middle or high school geometry lessons and interactive exploration, it helps students visualize how medians and special points behave as the triangle moves, and can be used by teachers to create interactive courseware.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[(s, (sqrt(3) * t)), s, -4, 13], t, -4, 13) → ListDots1
  2. Sequence(Sequence[(s + 1 / 2, (sqrt(3) * t) + sqrt(3) / 2), s, -4, 13], t, -4, 13) → ListDots2
  3. If(ShowChi, "顯示等距格線", "Show Isometric Grid") → TextIso
  4. If(ShowChi, "顯示方格線", "Show Square Grid") → TextSq
  5. If(ShowChi, IndexOf[SelectedElement[ListTriTypeC], ListTriTypeC], IndexOf[SelectedElement[ListTriTypeE], ListTriTypeE]) → TriType
  6. Polygon(Tri1Po1, Tri1Po2, Tri1Po3) → Tri1, Tri1Seg3, Tri1Seg1, Tri1Seg2
  7. Segment(Tri2Po1, Tri2Po2) → Tri2Seg1
  8. OrthogonalLine(Tri2Po1, Tri2Seg1) → Tri2AuxLine1
  9. Point(Tri2AuxLine1) → Tri2Po3
  10. Segment(Tri2Po2, Tri2Po3) → Tri2Seg2
  11. Segment(Tri2Po3, Tri2Po1) → Tri2Seg3
  12. Segment(Tri3Po1, Tri3Po2) → Tri3Seg1
  13. Midpoint(Tri3Po1, Tri3Po2) → Tri3AuxPo1
  14. OrthogonalLine(Tri3AuxPo1, Tri3Seg1) → Tri3AuxLine1
  15. Point(Tri3AuxLine1) → Tri3Po3
  16. Segment(Tri3Po2, Tri3Po3) → Tri3Seg2
  17. Segment(Tri3Po3, Tri3Po1) → Tri3Seg3
  18. Polygon(Tri4Po1, Tri4Po2, 3) → Tri4, Tri4Seg1, Tri4Seg2, Tri4Seg3, Tri4Po3
  19. Segment(Tri5Po1, Tri5Po2) → Tri5Seg1
  20. OrthogonalLine(Tri5Po1, Tri5Seg1) → Tri5AuxLine1
  21. Circle(Tri5Po1, Length[Tri5Seg1]) → Tri5AuxCir1
  22. Intersect(Tri5AuxCir1, Tri5AuxLine1, 2) → A
  23. Segment(A, Tri5Po1) → Tri5Seg2
  24. Segment(A, Tri5Po2) → Tri5Seg3

AI Drawing Prompt Reference

Draw a dynamic triangle with movable vertices or sliders to observe shape and position changes. Show triangle sides, vertices, medians, centroid, and orthocenter. Include random point generation, auxiliary lines, quadrilaterals, and parabolic elements. Add options to display isometric and square grids for interactive geometry exploration suitable for teaching.
The prompt above was compiled from the original drawing commands and is for reference only.