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Orthocenter and Rhombus Demo

Orthocenter and Rhombus Demo
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2015-10-22 09:46
TriangleOptimizationGeometric Construction
This example demonstrates the orthocenter's position in a triangle and its relation to a rhombus. Core math concepts include orthocenter, rhombus properties, vector operations, and geometric construction. Construction highlights involve commands like Polygon, Midpoint, Segment, Intersect, OrthogonalLine, Distance, Angle to draw triangles, rhombuses, and calculate the orthocenter. Suitable for high school mathematics teaching to understand triangle geometry and optimization problems.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(c) → D
  3. Midpoint(a) → E
  4. Midpoint(b) → F
  5. Segment(A, E) → d
  6. Segment(C, D) → e
  7. Segment(B, F) → f
  8. Intersect(d, e) → Centroid
  9. Polygon(A_1, B_1, C_1) → poly1_1, c_1, a_1, b_1
  10. Midpoint(c_1) → D_1
  11. Midpoint(a_1) → E_1
  12. Midpoint(b_1) → F_1
  13. OrthogonalLine(C_1, c_1) → g
  14. OrthogonalLine(A_1, a_1) → h
  15. OrthogonalLine(B_1, b_1) → i
  16. Intersect(g, h) → Orthocenter
  17. Distance(A, F) → distanceAF
  18. Midpoint(A, F) →
  19. Distance(F, C) → distanceFC
  20. Midpoint(F, C) →
  21. Distance(A, D) → distanceAD
  22. Midpoint(A, D) →
  23. Distance(D, B) → distanceDB
  24. Midpoint(D, B) →
  25. Distance(B, E) → distanceBE
  26. Midpoint(B, E) →
  27. Distance(E, C) → distanceEC
  28. Midpoint(E, C) →
  29. Distance(B, F) → distanceBF
  30. Midpoint(B, F) →
  31. Distance(A, E) → distanceAE
  32. Midpoint(A, E) →
  33. Distance(C, D) → distanceCD
  34. Midpoint(C, D) →
  35. Angle(A_1, B_1, C_1) → δ
  36. Angle(B_1, C_1, A_1) → ε
  37. Angle(C_1, A_1, B_1) → ζ
  38. Intersect(g, c_1) → G
  39. Intersect(h, a_1) → H
  40. Intersect(i, b_1) → I
  41. Angle(Orthocenter, G, B_1) → α
  42. Angle(Orthocenter, H, C_1) → β
  43. Angle(C_1, I, Orthocenter) → γ