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Medians and Areas

Medians and Areas
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2021-10-08 15:45
TriangleFunctionCoordinate Geometry
This example demonstrates the relationship between medians and areas in a triangle. Key mathematical concepts include medians of a triangle, area calculation, and piecewise functions. It is constructed using GeoGebra commands such as Line, Intersect, and Polygon. Suitable for middle school and above students to learn geometric construction and area calculation.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(B, C) → g
  3. Line(C, A) → h
  4. Line(A, D) → i
  5. Line(C, D) → j
  6. Line(B, D) → k
  7. Intersect(h, k) → B'
  8. Intersect(g, i) → A'
  9. Intersect(f, j) → C'
  10. Polygon(A, B', C') → t_1, c', a, b'
  11. Polygon(B, C', A') → t_2, a', b, l
  12. Polygon(B', A', C) → t_3, c, m, n
  13. Polygon(C', B', A') → t_4, p, q, r
  14. Polygon(A, B, C) → t, c_1, a_1, b_1

AI Drawing Prompt Reference

Draw a triangle ABC and its three medians. The medians intersect the sides of the triangle, forming smaller triangles. Connect these intersection points to find a central point. Show these figures to help understand the relationship between medians and area.
The prompt above was compiled from the original drawing commands and is for reference only.