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Pythagoras' Theorem Part 2

Pythagoras' Theorem Part 2
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2015-05-17 17:14
TriangleAngleGeometric Construction
In collections Euclid's proof of Pythagoras Theorem (proposition 47) Pythagoras' theorem Y10 Pythag & Trig
This example demonstrates the second part of Pythagoras' theorem by constructing the relationship between the sides of a right triangle. Key mathematical concepts include right triangles and Pythagoras' theorem. It uses GeoGebra commands such as Segment, OrthogonalLine, Point, Angle, Circle, Intersect, Polygon, and PointIn. Suitable for middle school and above students learning geometric construction.

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(A, I, B) → poly5, b_4, a_4, i_3
  49. Polygon(C, B, E) → poly6, e_3, c_4, b_5
  50. PointIn(poly5) → Pointpoly5
  51. PointIn(poly6) → Pointpoly6