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Pythagorean Theorem Proof - Square

Pythagorean Theorem Proof - Square
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2019-02-11 04:02
TriangleVectorGeometric Construction
This example demonstrates the proof of the Pythagorean Theorem. By constructing squares and triangles, it shows that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Commands used include Polygon, Segment, Intersect, Point, Rotate, Ray, OrthogonalLine, Vector, Translate, suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Segment(A, C) → j
  3. Segment(B, D) → k
  4. Intersect(j, k) → M
  5. Point(i) → E
  6. Rotate(E, 90°, M) → F
  7. Ray(F, B) → l
  8. OrthogonalLine(X, l) → a_8
  9. Rotate(F, 90°, M) → G
  10. Rotate(G, 90°, M) → H
  11. Segment(F, G) → c_5
  12. Segment(G, H) → c_3
  13. Segment(H, E) → c_4
  14. Segment(F, B) → a_1
  15. Segment(B, G) → b_8
  16. Segment(G, C) → a_3
  17. Segment(C, H) → b_3
  18. Segment(H, D) → a_4
  19. Segment(D, E) → b_4
  20. Vector(X, Y) → u
  21. Translate(F, u) → F'
  22. Translate(B, u) → B'
  23. Segment(F', B') → a_5
  24. Translate(A, u) → A'
  25. Translate(F, u) → F'_1
  26. Segment(A', F'_1) → b_7
  27. Translate(D, u) → D'
  28. Translate(E, u) → E'
  29. Segment(D', E') → b_5
  30. Polygon(D', A', 4) → poly2, m, n, p, q, I, J
  31. Segment(B', J) → r
  32. Segment(J, D') → s
  33. Segment(A', E') → t
  34. Polygon(F', B', 4) → poly3, a_7, b_1, c_1, d, K, L
  35. Segment(F', L) → e
  36. Segment(L, K) → f_1
  37. Segment(L, E') → g_1
  38. Segment(B', K) → a_6
  39. Segment(K, J) → i_1
  40. OrthogonalLine(L, s) → j_1
  41. Intersect(j_1, s) → N
  42. Segment(D', N) → b_6
  43. Segment(N, J) → l_1
  44. Segment(L, N) → m_1
  45. Segment(F', E') → n_1
  46. Segment(L, J) → p_1
  47. Segment(A, F) → b
  48. Segment(F, E) → c
  49. Segment(E, A) → a
  50. Polygon(E, F, G, H) → c_2, e_1, f_2, g_2, h_1
  51. Polygon(F', B', K, L) → a_2, f', b', k_1, l_2
  52. Polygon(E', L, N, D') → b_2, e', l_3, n_2, d'

AI Drawing Prompt Reference

Draw a right triangle ABC with AB as one of the legs, BC as the hypotenuse, and AC as the other leg. Construct squares on each side of the triangle. Rotate and translate these triangles to form two new squares, one with side length equal to BC and the other with side length equal to half the sum of AB and AC. Demonstrate the geometric proof of the Pythagorean theorem by showing that the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
The prompt above was compiled from the original drawing commands and is for reference only.