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Triangle Area by Hatem Dhaoui

Triangle Area by Hatem Dhaoui
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2017-10-08 15:38
TriangleCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of a triangle using geometric construction. Key mathematical concepts include the properties of triangles and the area formula. Using GeoGebra commands such as Polygon, Intersect, and Segment, a dynamic triangle can be constructed and its area can be calculated in real-time. Suitable for middle school and above students learning geometry and area calculation.

GeoGebra Commands & Parameters

  1. Polygon(n_2, n_3, n_4) → poly1, c, a, b
  2. OrthogonalLine(n_2, a) → d
  3. Intersect(a, d) → D
  4. Segment(n_2, D) → e
  5. Midpoint(n_3, n_2) → E
  6. Midpoint(n_4, n_2) → F
  7. Polygon(n_2, n_4, D) → poly2, d_1, a_1, c_1
  8. Polygon(n_2, n_3, D) → poly3, d_2, a_2, b_1
  9. Rotate(n_2, حرك, F) → A'
  10. Rotate(n_4, حرك, F) → C'
  11. Rotate(D, حرك, F) → D'
  12. Polygon(A', C', D') → poly2', d', a', c'
  13. Rotate(n_2, (-حرك), E) → A'_1
  14. Rotate(n_3, (-حرك), E) → B'
  15. Rotate(D, (-حرك), E) → D'_1
  16. Polygon(A'_1, B', D'_1) → poly3', d'_1, a'_1, b'
  17. Segment(n_2, n_3) → f
  18. Segment(n_3, D) → g
  19. Segment(D, n_4) → n_6
  20. Segment(n_4, n_2) → i
  21. Segment(C', D') → j
  22. Segment(D', A') → k
  23. Segment(A', C') → l
  24. Segment(B', D'_1) → m
  25. Segment(D'_1, A'_1) → n_1
  26. Segment(A'_1, B') → p
  27. Segment(n_2, D) → q
  28. Polygon(n_2, D', n_4) → poly4, c_2, a_3, d'_2
  29. Polygon(n_2, D'_1, n_3) → poly5, b_2, a_4, d'_3
  30. Angle(n_4, D, n_2) → β
  31. Segment(A, n) → r
  32. Line(C, g) → n_7
  33. Line(I, n_1) → s
  34. Line(n_2, n_7) → t
  35. Line(n_3, s) → e_1
  36. Intersect(t, s) → M
  37. Intersect(n_7, s) → N
  38. Intersect(n_7, e_1) → O
  39. Line(n_4, s) → f_1
  40. Intersect(n_7, f_1) → P
  41. Line(n_3, n_7) → g_1
  42. Intersect(s, g_1) → Q
  43. Vector(C, P) → u
  44. Vector(C, O) → v
  45. Vector(I, M) → w
  46. Vector(I, Q) → z
  47. Polygon(B, R, S, T) → poly6, b_3, r_1, s_1, t_1
  48. Polygon(B, R, S, T) → poly7, b_4, r_2, s_2, t_2
  49. Midpoint(n_2, D) → U

AI Drawing Prompt Reference

Draw a triangle ABC and calculate its area dynamically. First, draw triangle ABC, then construct auxiliary lines and point D through points A, B, and C. Next, use rotation and translation to construct a new triangle A'B'C', and calculate the area of both the original triangle ABC and the new triangle A'B'C'.
The prompt above was compiled from the original drawing commands and is for reference only.