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Pythagoras' Theorem Part 4

Pythagoras' Theorem Part 4
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2015-05-17 17:29
TriangleAngleGeometric Construction
In collections Euclid's proof of Pythagoras Theorem (proposition 47) Pythagoras' theorem
This example demonstrates the fourth part of Pythagoras' theorem, showing the relationship between the hypotenuse and the legs of a right triangle. Key mathematical concepts include right triangles and the application of Pythagoras' theorem. Using GeoGebra commands such as Segment, OrthogonalLine, and Point, a right triangle is constructed, and a polygon is drawn. Suitable for middle school and above students to learn geometric construction 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. 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. Segment(J, K) → l_1
  48. Polygon(C, B, E) → poly6, e_3, c_4, b_5
  49. Polygon(A, B, E, D) → poly5, a_4, b_4, e_4, d_3
  50. PointIn(poly5) → Pointpoly5
  51. PointIn(poly6) → Pointpoly6

AI Drawing Prompt Reference

Draw a right triangle to show the relationship between the hypotenuse and the legs. Construct a right triangle, mark the right-angle vertex, and draw the hypotenuse. Add two circles with the right-angle vertex as the center and radii equal to the leg lengths. Connect the circles with the hypotenuse to find intersection points. Finally, draw a polygon that includes these intersection points and the right-angle vertex to form a shape.
The prompt above was compiled from the original drawing commands and is for reference only.