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Pythagoras' Theorem Part 6

Pythagoras' Theorem Part 6
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2015-05-18 03:32
TriangleVectorGeometric Construction
In collections Euclid's proof of Pythagoras Theorem (proposition 47) Pythagoras' theorem
This example demonstrates the 6th part of Pythagoras' theorem, showing the relationship between the hypotenuse and the legs of a right triangle. Key mathematical concepts include the properties of right triangles and similarity transformations. Using GeoGebra commands such as Segment, OrthogonalLine, and Point, a dynamic geometric model is constructed. Suitable for middle school and above students to explore geometric transformations and Pythagoras' theorem.

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. Segment(A, J) → i_1
  39. Polygon(J, K, H, C) → poly1, j_1, k_1, h_2, c_2
  40. Polygon(C, A, F, G) → poly2, c_3, a_2, f_2, g_2
  41. PointIn(poly1) → Pointpoly1
  42. PointIn(poly2) → Pointpoly2

AI Drawing Prompt Reference

Draw a right triangle ABC with AB as the hypotenuse and AC and BC as the legs. Construct the altitude from C to AB, and use it to draw other lines and circles based on the properties of right triangles and similarity transformations. Finally, form two quadrilaterals and two triangles to explore Pythagoras' theorem.
The prompt above was compiled from the original drawing commands and is for reference only.