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Triangle Centroid Investigation

Triangle Centroid Investigation
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2014-11-19 22:17
TriangleCoordinate Geometry
This example demonstrates the properties of the centroid in a triangle, involving concepts such as the centroid, midpoints, segments, and circles. Using GeoGebra commands like Polygon, Midpoint, and Segment, one can observe how the centroid divides the medians of the triangle. Suitable for middle school and above students or teachers.

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(B, F) → d
  6. Segment(C, D) → e
  7. Segment(E, A) → f
  8. Intersect(d, e) → Centroid
  9. Segment(A, F) → g
  10. Segment(F, C) → h
  11. Segment(B, D) → i
  12. Segment(D, A) → j
  13. Segment(B, E) → k
  14. Segment(E, C) → l
  15. Segment(B, Centroid) → m
  16. Segment(Centroid, F) → n
  17. Segment(C, Centroid) → p
  18. Segment(Centroid, D) → q
  19. Segment(A, Centroid) → r
  20. Segment(Centroid, E) → s

AI Drawing Prompt Reference

Draw a triangle ABC, then find its three medians and their intersection point, which is the centroid of the triangle. First, draw the triangle, then find the midpoints of sides BC, CA, and AB, which are points D, E, and F respectively. Next, draw segments BF, CE, and AD, and they will intersect at a point, which is the centroid.
The prompt above was compiled from the original drawing commands and is for reference only.