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Proof Without Words: Pythagorean Theorem by Steve Phelps (5)

Proof Without Words: Pythagorean Theorem by Steve Phelps (5)
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2015-02-20 10:00
TriangleCoordinate GeometryGeometric ConstructionSlider Animation
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This is a dynamic demonstration of the Pythagorean Theorem using geometric construction. By dragging points and sliders, observe the relationship between the sides of a right triangle. This diagram proves that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The construction uses commands such as Point, Intersect, Polygon, CircleArc, Line, Segment, OrthogonalLine, Circle, If, Rotate, Dilate, Vector, Translate. Suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. Polygon(C, A, 4) → poly1, a, b, c, d, D, E
  4. Polygon(A, C, 4) → poly2, e, f, g, h, F, G
  5. CircleArc(B, H, A) → k
  6. Point(k) → I
  7. Line(A, I) → i
  8. Segment(I, C) → j
  9. OrthogonalLine(G, i) → l
  10. Intersect(i, l) → J
  11. Circle(J, Segment[I, A]) → p
  12. Intersect(p, i, 1) → K
  13. OrthogonalLine(K, i) → m
  14. Intersect(m, h) → L
  15. Polygon(A, I, C) → poly3, c_1, a_1, i_1
  16. Intersect(i, g) → M
  17. Polygon(C, I, M, F) → poly4, c_2, i_2, m_1, f_1
  18. Polygon(J, G, L, K) → poly5, j_1, g_1, l_1, k_1
  19. Polygon(J, G, M) → poly6, m_2, j_2, g_2
  20. Polygon(L, K, A) → poly7, a_2, l_2, k_2
  21. If(0 ≤ n ≤ 1, n - 0, If[n > 1, 1, 0]) → r1
  22. Rotate(L, (90° * r1), G) → L'
  23. Rotate(K, (90° * r1), G) → K'
  24. Rotate(A, (90° * r1), G) → A'
  25. Polygon(L', K', A') → poly7', a', l', k'
  26. If(1 ≤ n ≤ 2, n - 1, If[n > 2, 1, 0]) → r2
  27. Rotate(A, (-((90° * r2))), C) → A'_1
  28. Rotate(I, (-((90° * r2))), C) → I'
  29. Rotate(C, (-((90° * r2))), C) → C'
  30. Polygon(A'_1, I', C') → poly3', c', a'_1, i'
  31. If(2 ≤ n ≤ 3, 3 - n, If[n > 3, 0, 1]) → d1
  32. Dilate(K, d1, A) → K'_1
  33. Vector(K, K'_1) → u
  34. Translate(J, u) → J'
  35. Translate(G, u) → G'
  36. Translate(L, u) → L'_1
  37. Translate(K, u) → K'_2
  38. Polygon(J', G', L'_1, K'_2) → poly5', j', g', l'_1, k'_2
  39. Translate(J, u) → J'_1
  40. Translate(G, u) → G'_1
  41. Translate(M, u) → M'
  42. Polygon(J'_1, G'_1, M') → poly6', m', j'_1, g'_1
  43. If(2 ≤ n ≤ 3, n - 2, If[n > 3, 1, 0]) → r3
  44. Rotate(J'_1, (270° * r3), G') → N
  45. Rotate(G'_1, (270° * r3), G') → O
  46. Rotate(M', (270° * r3), G') → M''
  47. Polygon(N, O, M'') → poly6'', m'', n_1, o

AI Drawing Prompt Reference

Draw a right triangle with a dynamic demonstration proving the Pythagorean theorem. Show a square with side length equal to the sum of the squares of the two legs, and another square with side length equal to the hypotenuse. Observe the relationship between the sides by dragging points and sliders. Include rotations, translations, and dilations to prove the areas of the two squares are equal.
The prompt above was compiled from the original drawing commands and is for reference only.