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Dynamic Pythagoras Theorem Demonstration

Dynamic Pythagoras Theorem Demonstration
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2016-03-31 14:16
TriangleAngleGeometric Construction
This example demonstrates the Pythagorean theorem through a dynamic geometric figure. It shows that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. Key mathematical concepts include right triangles, the Pythagorean theorem, and angles. It uses commands such as Segment, OrthogonalLine, Point, Rotate, Intersect, Angle, Midpoint, Text, and Polygon in GeoGebra. Suitable for middle school and above students to learn geometry and proofs.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Point(b) → C
  4. Segment(A, C) → c
  5. Segment(C, B) → d
  6. Rotate(C, 90°, C) → C'
  7. Rotate(B, 90°, C) → B'
  8. Segment(C', B') → d'
  9. Rotate(C', 90°, B') → C''
  10. Rotate(B', 90°, B') → B''
  11. Segment(C'', B'') → d''
  12. Segment(C'', B) → e
  13. OrthogonalLine(B', b) → g
  14. Intersect(b, g) → D
  15. Segment(C, D) → f
  16. Segment(D, B') → h
  17. OrthogonalLine(C'', g) → i
  18. Intersect(g, i) → E
  19. Segment(B', E) → j
  20. Segment(E, C'') → k
  21. OrthogonalLine(B, i) → l
  22. Segment(E, C'') → m
  23. Intersect(i, l) → F
  24. Segment(C'', F) → n
  25. Segment(F, B) → p
  26. Angle(C, D, B') → α
  27. Angle(B', E, C'') → β
  28. Angle(B, F, C'') → γ
  29. Angle(d', d) → δ
  30. Angle(C, A, B) → ε
  31. Angle(C, B, C'') → ζ
  32. Angle(B'', C'', B) → η
  33. Angle(d'', d) → θ
  34. Intersect(d', d'') → H
  35. Angle(C, B, A) → κ
  36. Angle(B, C'', F) → λ
  37. Angle(f, d') → μ
  38. Angle(A, C, B) → ν
  39. Angle(D, B', C') → ξ
  40. Angle(B'', C'', E) → ο
  41. Angle(C'', B, F) → ρ
  42. Intersect(d', d'') → K
  43. Midpoint(k) → M
  44. Midpoint(n) → N
  45. Midpoint(p) → O
  46. Midpoint(a) → P
  47. Text(" a", M) → text9
  48. Text(" b", N) → text10
  49. Midpoint(c) → S
  50. Midpoint(f) → LL
  51. Midpoint(h) → U
  52. Midpoint(j) → V
  53. Midpoint(d'') → G
  54. Angle(G, H, V) → ι
  55. Point(Circle[V, 0.3844228700967704]) → I
  56. Polygon(V, I, J) → poly1, j_1, v, i_1
  57. Point(Circle[U, 0.29763004734908566]) → L
  58. Polygon(U, L, R) → poly2, r, u, l_1
  59. Point(Circle[LL, 0.333181955679241]) → T
  60. Polygon(LL, T, Z) → poly3, z_1, w, t
  61. Point(Circle[S, 0.44269092479036803]) → Q
  62. Text(text2, P) → text3
  63. Text(text1, O) → text4
  64. Text("a", L) → text7
  65. Text("a", Q) → text8
  66. Text("b", I) → text11
  67. Text("b", T) → text12
  68. Angle(C, H, G) → σ