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Median Invariants

Median Invariants
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2015-03-04 08:03
TriangleProbability & Statistics
This example demonstrates the invariance properties of the medians in a triangle. Key mathematical concepts include median lines, area, and statistical characteristics. Using GeoGebra commands such as Polygon, Midpoint, and Segment, a triangle is constructed and the changes in median lengths are observed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(A, C) → D
  3. Segment(B, D) → d
  4. Distance(A, B) → distanceAB
  5. Distance(B, C) → distanceBC
  6. Distance(C, D) → distanceCD
  7. Distance(C, A) → distanceCA
  8. Distance(A, D) → distanceAD
  9. PointIn(poly1) → Pointpoly1_1
  10. PointIn(poly1) → Pointpoly1_2
  11. PointIn(poly1) → Pointpoly1_3
  12. PointIn(poly1) → Pointpoly1_4
  13. Polygon(B, D, C) → poly2, c_1, b_1, d_1
  14. PointIn(poly1) → Pointpoly1_5
  15. PointIn(poly1) → Pointpoly1_6
  16. PointIn(poly1) → Pointpoly1_7
  17. PointIn(poly1) → Pointpoly1
  18. PointIn(poly2) → Pointpoly2
  19. Polygon(A, B, D) → poly3, d_2, a_1, b_2
  20. PointIn(poly3) → Pointpoly3

AI Drawing Prompt Reference

Draw a triangle ABC, find the midpoint D of AC, connect BD, measure the lengths of AB, BC, CD, CA, and AD, and observe the changes in points inside the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.