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Triangle Medians and Centroid Demonstration

Triangle Medians and Centroid Demonstration
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2012-05-30 16:53
TrianglePolygonGeometric Construction
① This example shows the three medians of a triangle intersecting at the centroid, and that the centroid divides each median in a 2:1 ratio. ② Core mathematical concepts: triangle, median, centroid (barycenter), segment ratio, geometric construction. ③ Construction highlights: Polygon to create the triangle, Midpoint to find side midpoints, Segment to draw medians, Intersect to locate the centroid, Distance and Text to measure and display the 2:1 ratio. ④ Suitable for middle‑school geometry (grades 7‑8) and high‑school review, as well as teacher demonstrations or student inquiry activities.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(a) → D
  3. Segment(A, D) → d
  4. Distance(B, D) → distanceBD
  5. Distance(D, C) → distanceDC
  6. Distance(B, C) → distanceBC
  7. Midpoint(b) → E
  8. Midpoint(c) → F
  9. Segment(C, F) → e
  10. Segment(B, E) → f
  11. Intersect(e, f) → G
  12. Distance(A, G) → distanceAG
  13. Distance(G, D) → distanceGD

AI Drawing Prompt Reference

Draw an arbitrary triangle, locate the midpoints of its three sides, connect each vertex to the opposite midpoint to form the three medians, mark their intersection as the centroid, then measure the distances from the centroid to each vertex and to the corresponding midpoint to illustrate that the centroid divides every median in a 2:1 ratio, clearly showing the geometric property.
The prompt above was compiled from the original drawing commands and is for reference only.