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Pythagoras Theorem Proof

Pythagoras Theorem Proof
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2013-12-30 05:38
TriangleCoordinate GeometryGeometric Construction
This example demonstrates a geometric proof of the Pythagorean Theorem. It involves the relationship between the sides of a right triangle. Using commands like Intersect, Point, Segment, Distance, etc., from the construction summary, it shows how to verify the theorem through geometric transformations. Suitable for middle school and above students to learn geometric proof methods.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Point(xAxis) → D
  4. Segment(B, C) → a
  5. Segment(C, D) → b
  6. Segment(D, A) → c
  7. Segment(A, B) → d
  8. Segment(L, K) → e
  9. Segment(K, I) → f
  10. Segment(I, E) → g
  11. Segment(E, L) → h
  12. Distance(B, K) → distanceBK
  13. Distance(K, C) → distanceKC
  14. Intersect(a, d) → F
  15. Intersect(a, e) → G
  16. Segment(F, G) → j
  17. Intersect(c, d) → H
  18. Intersect(d, e) → J
  19. Segment(H, J) → k
  20. Distance(H, J) → distanceHJ
  21. Intersect(b, c) → M
  22. Intersect(c, g) → N
  23. Segment(M, N) → l
  24. Intersect(a, b) → O
  25. Intersect(b, f) → P
  26. Segment(O, P) → m
  27. Distance(J, F) → distanceJF
  28. Distance(O, P) → distanceOP
  29. Distance(H, N) → distanceHN
  30. Distance(M, N) → distanceMN
  31. Distance(P, M) → distancePM
  32. Distance(J, G) → distanceJG
  33. Distance(G, P) → distanceGP
  34. Distance(P, N) → distancePN
  35. Distance(N, J) → distanceNJ
  36. Angle(A, B, C) → γ
  37. Angle(B, C, D) → δ
  38. Angle(L, K, I) → ε
  39. Angle(I, E, L) → ζ
  40. Angle(E, L, K) → η
  41. Angle(K, I, E) → θ
  42. Angle(D, A, B) → ι
  43. Angle(C, D, A) → κ

AI Drawing Prompt Reference

Draw a right triangle ABC with point A on the x-axis, point B on the y-axis, and point C in the first quadrant. Then draw sides AB, BC, and CA with their lengths. Next, draw the perpendicular bisector of AB, which intersects BC at F and AC at G, and draw FG. Repeat this process for other sides, find their intersections, and verify the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.