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Medians of a Triangle (Teacher Version) – Visualizing the Centroid and Median Pr

Medians of a Triangle (Teacher Version) – Visualizing the Centroid and Median Pr
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2020-01-03 21:19
TrianglePolygonCoordinate GeometryGeometric Construction
① This GeoGebra example dynamically demonstrates the three medians of a triangle and their intersection point (the centroid), showing key properties such as medians dividing the triangle into equal areas and the centroid dividing each median in a 2:1 ratio. ② Core mathematical concepts include triangle medians, centroid, midpoints, distance measurement, and geometric verification. ③ Construction details: The Polygon command creates triangle ABC, Midpoint generates midpoints D, E, F on each side, Segment connects vertices to opposite midpoints to form medians, Intersect finds the centroid G, Distance computes lengths from G to vertices and midpoints (e.g., kaugusDG, kaugusGC), and Text objects display these distances for easy observation of ratios. ④ Suitable for middle school geometry (triangle properties) and high school vector applications, ideal for teacher-led demonstrations or student exploration to understand the centroid theorem and geometric proofs.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Midpoint(A, B) → D
  3. Midpoint(B, C) → E
  4. Midpoint(A, C) → F
  5. Segment(D, C) → f
  6. Segment(B, F) → g
  7. Segment(A, E) → h
  8. Intersect(f, h) → G
  9. Distance(D, G) → kaugusDG
  10. Distance(G, C) → kaugusGC
  11. Distance(B, G) → kaugusBG
  12. Distance(G, F) → kaugusGF
  13. Distance(E, G) → kaugusEG
  14. Distance(G, A) → kaugusGA
  15. Polygon(D, G, A) → t2, a_1, d, g_1
  16. Polygon(G, A, F) → t3, f_1, g_2, a_2
  17. Polygon(G, F, C) → t4, c_1, g_3, f_2
  18. Polygon(G, C, E) → t5, e, g_4, c_2
  19. Polygon(G, E, B) → t6, b_1, g_5, e_1
  20. Polygon(B, D, G) → t7, g_6, b_2, d_1
  21. PointIn(t2) → Punktt2
  22. PointIn(t3) → Punktt3
  23. PointIn(t4) → Punktt4
  24. PointIn(t5) → Punktt5
  25. PointIn(t6) → Punktt6
  26. PointIn(t7) → Punktt7

AI Drawing Prompt Reference

Draw an arbitrary triangle with three vertices. Mark the midpoint of each side. Connect each vertex to the midpoint of the opposite side with a line segment, creating three medians that intersect at a single point, the centroid. Highlight the medians in distinct colors or styles)Skip the centroid point. Measure and display the distances from the centroid to each vertex and each midpoint, showing that the centroid divides each median in a 2:1 ratio. Divide the triangle into six smaller triangles by the medians and place a point inside each to indicate equal areas. The final figure should clearly illustrate the medians, centroid, and their geometric properties.
The prompt above was compiled from the original drawing commands and is for reference only.