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Pythagoras' Theorem Part 1

Pythagoras' Theorem Part 1
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2015-05-17 17:11
TriangleCoordinate GeometryGeometric Construction
In collections Euclid's proof of Pythagoras Theorem (proposition 47) Y10 Pythag & Trig
This example demonstrates the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Key mathematical concepts include right-angled triangles and the Pythagorean theorem. Using GeoGebra commands such as Segment, OrthogonalLine, Point, etc., a right-angled triangle is constructed to verify the theorem. Suitable for middle school and above students to learn geometric proofs and theorem verification.

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

AI Drawing Prompt Reference

Draw a right-angled triangle ABC with point A at the origin, point B on the x-axis, and point C on the y-axis. Construct the hypotenuse BC, then construct circles with centers at A, B, and C. Use perpendicular lines and intersections to verify the Pythagorean theorem, i.e., BC² = AB² + AC². Finally, draw auxiliary lines and polygons to demonstrate the division and recombination of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.