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Proof Without Words by Steve Phelps (5)

Proof Without Words by Steve Phelps (5)
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2015-02-22 07:59
TriangleCircleCoordinate GeometryGeometric ConstructionSlider Animation
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This example demonstrates the Pythagorean Theorem by dragging points and a slider. It illustrates the relationship between the lengths of the sides of a right triangle, involving core mathematical concepts like the Pythagorean Theorem, similar triangles, arithmetic mean, and difference. Construction highlights the use of GeoGebra commands such as If, Intersect, Point, Polygon, CircleArc, Dilate, Vector, Translate, OrthogonalLine. Suitable for middle school and above mathematics education, providing an intuitive understanding and verification of geometric theorems.

GeoGebra Commands & Parameters

  1. If(1 ≤ n ≤ 2, 2 - n, If[n > 2, 0, 1]) → d2
  2. Intersect(xAxis, yAxis) → B
  3. Point(xAxis) → A
  4. Polygon(C, A, 4) → poly3, j, k, l, m, J, K
  5. CircleArc(B, D, A) → c
  6. Point(c) → E
  7. Polygon(A, E, 4) → poly1, a, b, d, e, F, G
  8. Polygon(E, C, 4) → poly2, f, g, h, i, H, I
  9. If(0 ≤ n ≤ 1, 1 - n, If[n > 1, 0, 1]) → d1
  10. If(2 ≤ n ≤ 3, 3 - n, If[n > 3, 0, 1]) → d3
  11. If(3 ≤ n ≤ 4, 4 - n, If[n > 4, 0, 1]) → d4
  12. Dilate(E, d1, A) → E'
  13. Vector(E, E') → u
  14. Translate(I, u) → I'
  15. OrthogonalLine(A, j) → p
  16. OrthogonalLine(H, p) → q
  17. Intersect(p, q) → L
  18. Dilate(I', d2, L) → I''
  19. Vector(I', I'') → v
  20. Translate(H, v) → H'
  21. Dilate(C, d3, K) → C'
  22. Vector(C, C') → w
  23. Translate(H', w) → H''
  24. Translate(E', w) → E''
  25. Translate(I'', w) → I'''
  26. Polygon(I''', E'', C', H'') → poly4, i''', e'', c', h''
  27. Dilate(E, d4, C) → E'_1
  28. Vector(E, E'_1) → r
  29. Translate(F, r) → F'
  30. OrthogonalLine(C, j) → s
  31. OrthogonalLine(G, s) → t
  32. Intersect(s, t) → M
  33. If(4 ≤ n ≤ 5, 5 - n, If[n > 5, 0, 1]) → d5
  34. Dilate(F', d5, M) → F''
  35. Vector(F', F'') → u_1
  36. Translate(G, u_1) → G'
  37. If(5 ≤ n ≤ 6, 6 - n, If[n > 6, 0, 1]) → d6
  38. Dilate(A, d6, I''') → A'
  39. Vector(A, A') → v_1
  40. Translate(E'_1, v_1) → N
  41. Translate(F'', v_1) → F'''
  42. Translate(G', v_1) → G''
  43. Polygon(A', G'', F''', N) → poly5, a', g'', f''', n_1