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Triangle Centroid Exploration with Dynamic Colors

Triangle Centroid Exploration with Dynamic Colors
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2015-03-07 12:30
TriangleCoordinate GeometryGeometric Construction
This example demonstrates a triangle centroid inquiry activity using dynamic colors in GeoGebra. Key math concepts include the centroid of a triangle, logic, and geometric construction. Commands used include Polygon, Segment, If, Line, OrthogonalLine, Intersect, PointIn, and Element. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Segment(D, B) → d
  3. Segment(D, A) → e
  4. Segment(D, C) → f
  5. If((e ≤ d) ∧ (e ≤ f), 1, 0) → red
  6. If((d ≤ e) ∧ (d ≤ f), 1, 0) → blue
  7. If((f ≤ e) ∧ (f ≤ d), 1, 0) → yel
  8. Line(A, B) → h
  9. Line(B, C) → i
  10. Line(C, A) → j
  11. OrthogonalLine(E, h) → k
  12. OrthogonalLine(E, j) → l
  13. OrthogonalLine(E, i) → m
  14. Intersect(l, j) → F
  15. Intersect(k, h) → G
  16. Intersect(m, i) → H
  17. Segment(G, E) → n
  18. Segment(E, H) → p
  19. Segment(E, F) → q
  20. If((n ≤ p) ∧ (n ≤ q), 1, 0) → pur
  21. If((p ≤ n) ∧ (p ≤ q), 1, 0) → gre
  22. If((q ≤ n) ∧ (q ≤ p), 1, 0) → ora
  23. PointIn(poly1) → P
  24. Element(list1, 1, 1) → r2
  25. Element(list1, 2, 1) → s2
  26. Element(list1, 3, 1) → t2
  27. If((r2 ≥ s2) ∧ (r2 ≥ t2), 1, 0) → red3
  28. If((t2 ≥ s2) ∧ (t2 ≥ r2), 1, 0) → yel3
  29. If((s2 ≥ t2) ∧ (s2 ≥ r2), 1, 0) → blu3

AI Drawing Prompt Reference

Draw a triangle with dynamic colors for its sides based on their lengths. From each vertex, draw lines to the opposite sides, meeting at the centroid. Draw perpendiculars from the centroid to each side, and mark their intersections with different colors. Finally, dynamically change the colors of these intersections based on their distances from the centroid.
The prompt above was compiled from the original drawing commands and is for reference only.