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Pythagorean Theorem Algebraic Proof

Pythagorean Theorem Algebraic Proof
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2014-01-02 06:21
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the algebraic proof of the Pythagorean Theorem. It involves core mathematical concepts such as the Pythagorean Theorem, Tree Diagrams, Rational Numbers, Histograms, Tangent Function, and Polygons. The construction uses GeoGebra commands like Intersect, Segment, Distance, and Angle. It is suitable for high school students learning and understanding the algebraic proof of the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Segment(B, C) → b
  3. Segment(C, D) → b_1
  4. Segment(D, A) → c
  5. Segment(A, B) → d
  6. Segment(L, K) → e
  7. Segment(K, I) → f
  8. Segment(I, E) → g
  9. Segment(E, L) → h
  10. Distance(B, K) → distanceBK
  11. Distance(K, C) → distanceKC
  12. Intersect(b, d) → F
  13. Intersect(b, e) → G
  14. Segment(F, G) → j
  15. Intersect(c, d) → H
  16. Intersect(d, e) → J
  17. Segment(H, J) → k
  18. Distance(H, J) → distanceHJ
  19. Intersect(c, g) → N
  20. Segment(M, N) → l
  21. Intersect(b, b_1) → O
  22. Intersect(b_1, f) → P
  23. Segment(O, P) → m
  24. Distance(J, F) → distanceJF
  25. Distance(O, P) → distanceOP
  26. Distance(H, N) → distanceHN
  27. Distance(M, N) → distanceMN
  28. Distance(P, M) → distancePM
  29. Distance(J, G) → distanceJG
  30. Distance(G, P) → distanceGP
  31. Distance(P, N) → distancePN
  32. Distance(N, J) → distanceNJ
  33. Angle(A, B, C) → γ
  34. Angle(B, C, D) → δ
  35. Angle(L, K, I) → ε
  36. Angle(I, E, L) → ζ
  37. Angle(E, L, K) → η
  38. Angle(K, I, E) → θ
  39. Angle(D, A, B) → ι
  40. Angle(C, D, A) → κ