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Proof Without Words: Pythagorean Theorem by Steve Phelps (3)

Proof Without Words: Pythagorean Theorem by Steve Phelps (3)
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2015-02-09 07:43
TriangleVectorCoordinate Geometry
This example visually demonstrates the Pythagorean Theorem by dragging points and sliders. It involves concepts like rectangles and vectors. Using GeoGebra commands such as constructing rectangles, rotating, and translating, it dynamically shows that the area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two sides. Suitable for middle school and above students learning geometric proofs.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. CircleArc(B, D, A) → c
  4. Point(c) → E
  5. Polygon(A, E, 4) → poly1, a, b, d, e, F, G
  6. Polygon(E, C, 4) → poly2, f, g, h, i, H, I
  7. Polygon(A, C, 4) → poly3, j, k, l, m, J, K
  8. Intersect(b, m) → L
  9. Intersect(i, l) → M
  10. Polygon(A, G, F, L) → poly4, a_1, g_1, f_1, l_1
  11. Polygon(M, I, J) → poly5, j_1, m_1, i_1
  12. Polygon(J, C, H) → poly6, h_1, j_2, c_1
  13. Polygon(A, E, L) → poly7, l_2, a_2, e_1
  14. Polygon(E, M, J, C) → poly8, e_2, m_2, j_3, c_2
  15. If(n < 1, n, 1) → r1
  16. Rotate(A, (-(((r1 * 90))°)), A) → A'
  17. Rotate(G, (-(((r1 * 90))°)), A) → G'
  18. Rotate(F, (-(((r1 * 90))°)), A) → F'
  19. Rotate(L, (-(((r1 * 90))°)), A) → L'
  20. Polygon(A', G', F', L') → poly4', a', g', f', l'
  21. Dilate(J, If[1 ≤ n < 2, 2 - n, If[n ≥ 2, 0, 1]], C) → J'
  22. Vector(J, J') → u
  23. Translate(M, u) → M'
  24. Translate(I, u) → I'
  25. Translate(J, u) → J'_1
  26. Polygon(M', I', J'_1) → poly5', j'_1, m', i'
  27. Midpoint(A, J) → N
  28. Vector(A, L) → v
  29. Translate(C, v) → C'
  30. Vector(A, E) → w
  31. Translate(C, w) → C'_1
  32. Polygon(C, C', C'_1) → poly9, c'_1, c_3, c'
  33. Polygon(C', J, H, C'_1) → poly10, c'_2, j_4, h_2, c'_3
  34. Dilate(J, If[2 ≤ n < 3, 3 - n, If[n ≥ 3, 0, 1]], K) → J'_2
  35. Vector(J, J'_2) → p
  36. Translate(C', p) → C''
  37. Translate(J, p) → J'_3
  38. Translate(H, p) → H'
  39. Translate(C'_1, p) → O
  40. Polygon(C'', J'_3, H', O) → poly10', c'', j'_3, h', o
  41. If(3 ≤ n ≤ 4, n - 3, 0) → r2
  42. Rotate(C, (-(((r2 * 90))°)), J) → C'_2
  43. Rotate(C', (-(((r2 * 90))°)), J) → C''_1
  44. Rotate(C'_1, (-(((r2 * 90))°)), J) → P
  45. Polygon(C'_2, C''_1, P) → poly9', p_1, c'_4, c''_1