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Pythagoras' Theorem Part 7

Pythagoras' Theorem Part 7
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2015-05-18 03:33
TriangleTrigonometryCoordinate GeometryIntegralGeometric Construction
In collections Euclid's proof of Pythagoras Theorem (proposition 47) Pythagoras' theorem
This example demonstrates the application and verification of Pythagoras' theorem in specific geometric contexts. It involves core mathematical concepts such as Pythagoras' theorem, coordinate geometry, symmetry, and integral calculus. The construction uses GeoGebra commands like Segment, OrthogonalLine, Point, Angle, Circle, Intersect, Polygon, and PointIn to build geometric figures and analyze their properties. Suitable for high school and above learners to deepen their understanding of geometric theorems and computational methods.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Point(b) → C
  4. Segment(C, A) → c
  5. Segment(C, B) → d
  6. Angle(B, A, C) → α
  7. Circle(B, A) → e
  8. Circle(A, B) → f
  9. OrthogonalLine(B, a) → g
  10. OrthogonalLine(A, a) → h
  11. Intersect(f, h, 1) → D
  12. Intersect(e, g, 1) → E
  13. Segment(D, E) → i
  14. Segment(B, A) → j
  15. Segment(A, D) → k
  16. Segment(E, B) → l
  17. Circle(A, C) → p
  18. Circle(C, A) → q
  19. OrthogonalLine(A, c) → m
  20. Intersect(p, m, 1) → F
  21. OrthogonalLine(C, c) → n
  22. Intersect(q, n, 1) → G
  23. OrthogonalLine(C, d) → r
  24. OrthogonalLine(B, d) → s
  25. Circle(B, C) → t
  26. Circle(C, B) → c_1
  27. Intersect(c_1, r, 2) → H
  28. Intersect(t, s, 2) → I
  29. Segment(B, I) → a_1
  30. Segment(I, H) → b_1
  31. Segment(H, C) → d_1
  32. Segment(C, G) → e_1
  33. Segment(F, A) → f_1
  34. Segment(F, G) → g_1
  35. OrthogonalLine(A, d) → h_1
  36. Intersect(h_1, d) → J
  37. Intersect(h_1, b_1) → K
  38. Polygon(J, K, H, C) → poly1, j_1, k_1, h_2, c_2
  39. Polygon(A, C, G, F) → poly2, a_2, c_3, g_2, f_2
  40. Segment(A, J) → i_1
  41. Polygon(J, B, I, K) → poly3, j_2, b_2, i_2, k_2
  42. Polygon(A, D, E, B) → poly4, a_3, d_2, e_2, b_3
  43. PointIn(poly1) → Pointpoly1
  44. PointIn(poly2) → Pointpoly2
  45. PointIn(poly3) → Pointpoly3
  46. PointIn(poly4) → Pointpoly4
  47. Polygon(C, B, I, H) → poly5, c_4, b_4, i_3, h_3

AI Drawing Prompt Reference

Draw a right triangle ABC with point A at the origin, point B on the x-axis, and point C on the y-axis. Construct the perpendicular bisectors of AB, BC, and CA, intersecting at points D, E, and F. Use these perpendicular bisectors to construct squares and rectangles, and connect the points to form multiple polygons such as quadrilateral ABIF, quadrilateral ACGF, and quadrilateral BIKH.
The prompt above was compiled from the original drawing commands and is for reference only.