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Dynamic Triangle Transformations

Dynamic Triangle Transformations
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2020-11-07 12:53
TrianglePolygonGeometric Construction
This example demonstrates the dynamic transformations of triangles. Key mathematical concepts include triangle transformations and polygon construction. Using GeoGebra commands such as Sequence, If, and Polygon, it shows the movement, rotation, and scaling of triangles. Suitable for middle school and above students to learn geometric transformations and dynamic graphics.

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 geometry figure on a coordinate plane with an optional isometric grid or square grid. Construct two sets of points forming an equilateral-triangle shape and connect each triple of points to make closed triangular polygons. For a second triangle, draw a segment between two of its vertices, then construct the perpendicular line through one vertex to that segment, and take a new intersection point to connect it back to the triangle’s relevant vertices with segments. For another triangle, take the midpoint of a segment between two vertices, draw the perpendicular line to the corresponding side through that midpoint, and create a point on that line. Finally, draw a circle centered at a triangle vertex with radius equal to the length of the chosen side, intersect it with the perpendicular auxiliary line, then connect the intersection point to the corresponding two vertices to form the key related segments, illustrating dynamic triangle transformations.
The prompt above was compiled from the original drawing commands and is for reference only.