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Medians and Relative Areas in a Triangle

Medians and Relative Areas in a Triangle
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2016-06-26 20:29
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the invariance of relative areas formed by medians in a triangle. Key math concepts include triangle area, median properties, and relative area ratios. Construction involves Polygon, Midpoint, Segment, and Intersect commands to create triangles, midpoints, medians, and intersecting points, forming multiple sub-triangles. Suitable for high school mathematics education, helping students understand the median theorem and area relationships, and as practice in geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → S_{ABC}, c, a, b
  2. Midpoint(a) → D
  3. Midpoint(b) → E
  4. Midpoint(c) → F
  5. Segment(A, E) → f
  6. Segment(E, C) → g
  7. Segment(C, D) → h
  8. Segment(D, B) → i
  9. Segment(B, F) → j
  10. Segment(F, A) → k
  11. Segment(A, D) → l
  12. Segment(B, E) → m
  13. Intersect(l, m) → G
  14. Segment(F, C) → n
  15. Polygon(B, D, G) → S_1, g_1, b_1, d
  16. Polygon(G, D, C) → poly1, c_1, g_2, d_1
  17. Polygon(G, C, E) → poly2, e, g_3, c_2
  18. Polygon(A, E, G) → poly3, g_4, a_1, e_1
  19. Polygon(A, G, F) → poly4, f_1, a_2, g_5
  20. Polygon(F, G, B) → poly5, b_2, f_2, g_6