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Map of US - 4 Triangle Centers Exploration

Map of US - 4 Triangle Centers Exploration
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2015-08-11 04:57
TriangleCoordinate GeometryGeometric Construction
This example uses a map of the US to guide students in exploring the four important centers of a triangle: centroid, orthocenter, incenter, and circumcenter. Students will construct the midpoints, angle bisectors, and altitudes of a triangle to form conjectures about the positions of these centers. Commands used include Polygon, Midpoint, Segment, Intersect, LineBisector, AngularBisector, and OrthogonalLine. Suitable for middle school and above students for geometric construction and exploration.

GeoGebra Commands & Parameters

  1. Polygon(C, D, E) → poly1, e, c, d
  2. Midpoint(D, E) → F
  3. Midpoint(E, C) → G
  4. Midpoint(C, D) → H
  5. Segment(C, F) → a
  6. Segment(D, G) → b
  7. Segment(E, H) → f
  8. Intersect(a, b) → Centroid
  9. LineBisector(C, D) → g
  10. LineBisector(D, E) → h
  11. LineBisector(E, C) → i
  12. Intersect(g, h) → Circumcenter
  13. AngularBisector(E, D, C) → j
  14. AngularBisector(C, E, D) → k
  15. AngularBisector(D, C, E) → l
  16. Intersect(j, k) → Incenter
  17. OrthogonalLine(E, e) → m
  18. OrthogonalLine(C, c) → n
  19. OrthogonalLine(D, d) → p
  20. Intersect(m, n) → Orthocenter