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Important Points of a Triangle

Important Points of a Triangle
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2014-02-28 00:13
TriangleCoordinate GeometryGeometric Construction
This example uses the locations of airports in three cities to explore important points of a triangle, such as the centroid, orthocenter, and incenter. Through a real-life scenario, students can intuitively understand these concepts. Commands used include Intersect, Segment, Midpoint, AngularBisector, Circle, and Polygon. Suitable for middle and high school students learning geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Segment(B, AIRPORT) → beirut
  3. Segment(D, AIRPORT) → damascus
  4. Segment(AIRPORT, C) → amman
  5. Segment(B, D) → t1
  6. Segment(D, C) → t2
  7. Segment(B, C) → t3
  8. Midpoint(t3) → M1
  9. Midpoint(t2) → M2
  10. Midpoint(t1) → M3
  11. Segment(M2, B) → med2
  12. Segment(C, M3) → med3
  13. Segment(M1, D) → med1
  14. Intersect(med3, med2) → CENTROID
  15. OrthogonalLine(D, t3) → alt1
  16. OrthogonalLine(B, t2) → alt2
  17. OrthogonalLine(C, t1) → alt3
  18. Intersect(alt1, alt2) → ORTHOCENTER
  19. AngularBisector(t3, t2) → angb1, angbhelp1
  20. AngularBisector(t1, t2) → angbhelp2, angb2
  21. AngularBisector(t3, t1) → angb3, angbhelep3
  22. Intersect(angb2, angb1) → INCENTER
  23. OrthogonalLine(INCENTER, t1) → angbhelp5
  24. Intersect(t1, angbhelp5) → ANGBHELP4
  25. Circle(INCENTER, ANGBHELP4) → inscribed
  26. Midpoint(t3) → MP1
  27. Midpoint(t2) → MP2
  28. Midpoint(t1) → MP3
  29. OrthogonalLine(MP1, t3) → pbis1
  30. OrthogonalLine(MP2, t2) → pbis3
  31. OrthogonalLine(MP3, t1) → pbis2
  32. Intersect(pbis3, pbis1) → CIRCUMCENTER
  33. Circle(CIRCUMCENTER, D) → circumscribed
  34. Polygon(B, D, 3.0) → poly1, f, b_1, d_1, E
  35. Polygon(D, C, 3.0) → poly2, g, d_2, c_1, F
  36. Polygon(C, B, 3.0) → poly3, h, c_2, b_2, G
  37. Circle(D, F, C) → c1
  38. Circle(G, C, B) → c2
  39. Circle(B, E, D) → c3
  40. Intersect(c3, c1) → H, LEASTDISTANCE, ,
  41. Intersect(pbis3, pbis1) → Circumcenter
  42. Intersect(angb1, med3) → J
  43. Intersect(angb2, angb3) → Incenter
  44. Intersect(alt2, alt1) → Orthocenter
  45. Intersect(alt2, med2) → M
  46. Intersect(med3, med1) → Centroid
  47. Intersect(c3, c1, 2.0) → LeastDistance