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G_8.07 Area of Triangles

G_8.07 Area of Triangles
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2022-08-12 13:00
TriangleComplex NumberGeometric Construction
This example demonstrates the calculation of triangle area and geometric construction methods. Key mathematical concepts include the area formula for triangles, geometric construction techniques, and the application of complex numbers in geometry. Construction involves using GeoGebra commands such as Polygon, Midpoint, Segment, OrthogonalLine, etc. to create triangles and related figures. Suitable for middle school or high school students learning geometry fundamentals and complex number applications.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c_2, a, b_3
  2. Midpoint(b_3) → D
  3. Segment(A, D) → i
  4. Segment(D, C) → j
  5. Segment(C, B) → k
  6. Segment(B, A) → l
  7. Line(B, C) → f
  8. Line(B, A) → h_1
  9. Line(A, C) → n
  10. OrthogonalLine(A, f) → p
  11. OrthogonalLine(B, n) → q
  12. OrthogonalLine(C, h_1) → r
  13. Intersect(f, p) → E
  14. Intersect(n, q) → F
  15. Intersect(h_1, r) → G
  16. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], E) → A'_1
  17. Segment(A, A'_1) → h
  18. Polygon(B, E, A) → poly2, a_1, b_1, e
  19. Polygon(E, A, C) → poly3, c_1, e_1, a_2
  20. Angle(A, E, B) → β
  21. Polygon(B, E, A) → poly4, a_3, b_2, e_2
  22. Dilate(B, If[0 < d ≤ 1, 1 - d, 0], E) → B'_1
  23. Dilate(B, If[0 < d ≤ 1, 1 - d, 0], A) → B'_2
  24. Segment(B, B'_1) → h_2
  25. Segment(B, B'_2) → c
  26. Segment(A, C) → b
  27. Angle(A, E, B) → γ

AI Drawing Prompt Reference

Draw triangle ABC, then construct its median AD and a line perpendicular to BC passing through A. Next, construct the altitudes and medians, use the properties of similar triangles to construct points E, F, and G, and finally use these points to construct new triangles and segments, calculating the area of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.