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Constructing a Triangle with its Medians

Constructing a Triangle with its Medians
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2020-05-20 05:28
TriangleCircleCoordinate GeometryGeometric Construction
This example demonstrates how to construct a triangle given its medians. Key math concepts include medians, midpoints, triangle area, and geometric constructions. GeoGebra commands used are Point, Circle, Intersect, Midpoint, Segment, Area, and LaTeX. Suitable for middle school and above students to learn about median properties and construction techniques.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a']) → D
  2. Point(Vector[A, D], 2 / 3) → G
  3. Point(D, Vector[G, D]) → D'
  4. Circle(D', (2 / 3 * b')) → d
  5. Circle(G, (2 / 3 * c')) → c1
  6. Intersect(c1, d) → C, H, ,
  7. Point(D, Vector[C, D]) → B
  8. Midpoint(A, B) → F
  9. Midpoint(A, C) → E
  10. Segment(A, D) → f
  11. Segment(B, E) → g
  12. Segment(C, F) → h
  13. Point(Vector[B, E], 2 / 3) → G'
  14. Point(Vector[C, F], 2 / 3) → G''
  15. Segment(B, C) → b
  16. Segment(A, C) → c
  17. Segment(A, B) → a
  18. Area(Polygon[A, B, C]) → S
  19. LaTeX(S, true, true) → text1