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Visual Proof of Pythagorean Theorem by sks23cu

Visual Proof of Pythagorean Theorem by sks23cu
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2012-03-30 01:15
TriangleCircleVectorFunctionGeometric Construction
In collections Area Demonstrations
This example visually demonstrates the Pythagorean theorem using dynamic geometry. It 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. Key mathematical concepts include right triangles, the Pythagorean theorem, and geometric construction. The construction uses commands such as Segment, Point, Rotate, Circle, Intersect, Polygon, Vector, Translate, and more. Suitable for middle school and above students and teachers.

GeoGebra Commands & Parameters

  1. Segment(S, R) → a
  2. Point(a) → Q
  3. Dilate(S, 1 - slide, Q) → A'_1
  4. Rotate(R, 90*°, S) → D
  5. Segment(S, D) → b
  6. Segment(S, Q) → c
  7. Segment(Q, R) → d
  8. Rotate(S, 270*°, R) → C_1
  9. Segment(R, C_1) → e
  10. Segment(C_1, D) → f
  11. Circle(C_1, d) → g
  12. Intersect(g, e, 1) → F
  13. Circle(D, d) → h
  14. Circle(S, d) → k
  15. Intersect(h, f, 1) → G
  16. Intersect(k, b, 1) → H
  17. Segment(F, G) → j
  18. Segment(G, H) → l
  19. Segment(H, Q) → m
  20. Polygon(Q, R, F) → poly1, f_1, e_1, b_1
  21. Polygon(Q, S, H) → poly2, h_1, e_2, a_2
  22. Rotate(Q, -rotate, Q) → E'
  23. Rotate(S, -rotate, Q) → A'
  24. Rotate(H, -rotate, Q) → H'
  25. Polygon(E', A', H') → poly2', h', e', a'
  26. Polygon(G, D, H) → poly3, h_2, g_1, d_1
  27. Polygon(G, F, C_1) → poly4, c_1, g_2, f_2
  28. Rotate(G, rotate, G) → G'
  29. Rotate(D, rotate, G) → D'
  30. Rotate(H, rotate, G) → H'_1
  31. Polygon(G', D', H'_1) → poly3', h'_1, g', d'
  32. Vector(Q, A'_1) → u
  33. Translate(E', u) → E''
  34. Translate(A', u) → A''
  35. Translate(H', u) → H''
  36. Polygon(E'', A'', H'') → poly2'', h'', e'', a''
  37. Translate(Q, u) → E'_1
  38. Translate(R, u) → B'
  39. Translate(F, u) → F'
  40. Polygon(E'_1, B', F') → poly1', f', e'_1, b'
  41. Midpoint(b') → I
  42. Midpoint(e'_1) → J
  43. Midpoint(f') → L
  44. Midpoint(c_1) → E
  45. Midpoint(f_2) → N
  46. Midpoint(g_2) → O
  47. Midpoint(g') → A
  48. Midpoint(e'') → B
  49. Midpoint(h'_1) → C
  50. Midpoint(d') → K
  51. Midpoint(a'') → M