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Special Points and Lines in a Triangle by Chan So Ying

Special Points and Lines in a Triangle by Chan So Ying
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2016-12-07 09:16
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the relationship between special points and lines in a triangle. By dragging the triangle's vertices, you can observe how different types of special lines (such as angle bisectors, medians, altitudes) and special points (such as the orthocenter, incenter, circumcenter, centroid) change. The construction uses GeoGebra commands like Polygon, AngularBisector, Midpoint, Line, Intersect, Segment, LineBisector, OrthogonalLine, and Circle. Suitable for middle school and above students learning triangle geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. AngularBisector(c, b) → d, e
  3. Midpoint(a) → D
  4. Line(A, D) → f
  5. Intersect(e, a) → E
  6. Segment(A, E) → g
  7. Segment(A, D) → i
  8. LineBisector(a) → k
  9. OrthogonalLine(A, a) → m
  10. Midpoint(a) → F
  11. Line(C, B) → p
  12. Intersect(m, p) → G
  13. Intersect(a, g) → H
  14. AngularBisector(A, C, B) → r
  15. AngularBisector(C, B, A) → s
  16. Intersect(r, c) → I
  17. Intersect(s, b) → J
  18. Segment(I, C) → t
  19. Segment(J, B) → a_1
  20. Intersect(t, a_1) → K
  21. OrthogonalLine(K, c) → b_1
  22. Intersect(b_1, c) → L
  23. Circle(K, L) → c_1
  24. LineBisector(c) → d_1
  25. LineBisector(b) → e_1
  26. Intersect(d_1, c) → M
  27. Intersect(e_1, b) → N
  28. Intersect(k, d_1) → O
  29. Circle(O, A) → g_1
  30. Midpoint(c) → P
  31. Midpoint(b) → Q
  32. Segment(B, Q) → j_1
  33. Segment(C, P) → k_1
  34. Intersect(i, j_1) → R
  35. OrthogonalLine(B, b) → p_1
  36. OrthogonalLine(C, c) → q_1
  37. Intersect(p_1, q_1) → S

AI Drawing Prompt Reference

Draw a triangle and display its angle bisectors, medians, altitudes, centroid, orthocenter, incenter, and circumcenter. Observe how these special points and lines change as you drag the vertices of the triangle. Start by drawing the triangle, then construct the angle bisectors and medians for each side, finding the midpoints and feet of the altitudes. Locate the centroid, orthocenter, incenter, and circumcenter, and draw the circumcircle and nine-point circle. Finally, connect the centroid to each vertex and show the relationships between the orthocenter, incenter, and circumcenter.
The prompt above was compiled from the original drawing commands and is for reference only.