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Proof Without Words by Steve Phelps (14)

Proof Without Words by Steve Phelps (14)
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2015-02-03 03:19
TriangleCircleGeometric Construction
In collections Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster Proofs Without Words Proofs Without Words
This is a geometric figure demonstrating the Pythagorean Theorem without words. By dragging points, you can observe the relationship between different geometric elements. It shows that in a right-angled triangle, 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, circle arc, segment, mirror, polygon, etc., in GeoGebra. Suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → C
  3. CircleArc(C, B, A) → c
  4. Point(c) → D
  5. Segment(A, D) → a
  6. Mirror(A, C) → A'
  7. Segment(D, A') → b
  8. Segment(A', A) → d
  9. Polygon(A, D, 4) → poly1, e, f, g, h, E, F
  10. Polygon(D, A', 4) → poly2, i, j, k, l, G, H
  11. Polygon(A', A, 4) → poly3, m, n, p, q, I, J
  12. Segment(D, G) → r
  13. Segment(F, D) → s
  14. Ray(I, A) → t
  15. Ray(J, A') → a_1
  16. Midpoint(s) → K
  17. Midpoint(r) → L
  18. Intersect(s, t) → M
  19. Intersect(r, a_1) → N
  20. Mirror(M, K) → M'
  21. Mirror(N, L) → N'
  22. Polygon(D, N, A') → poly4, a', d_1, n_1
  23. Polygon(N', H, G) → poly5, g_1, n', h_1
  24. Polygon(D, N', H) → poly6, h_2, d_2, n'_1
  25. Polygon(G, N, A') → poly7, a'_1, g_2, n_2
  26. Polygon(A, M, F) → poly8, f_1, a_2, m_1
  27. Polygon(M', E, D) → poly9, d_3, m', e_1
  28. Polygon(F, E, M') → poly10, m'_1, f_2, e_2
  29. Polygon(M, D, A) → poly11, a_3, m_2, d_4
  30. Vector(A', J) → u
  31. Vector(H, A) → v
  32. Centroid(poly4) → O
  33. Centroid(poly5) → P
  34. Translate(D, u) → D'
  35. Translate(N, u) → N'_1
  36. Translate(A', u) → A''
  37. Polygon(D', N'_1, A'') → poly4', a'', d', n'_2
  38. Translate(N', v) → N''
  39. Translate(H, v) → H'
  40. Translate(G, v) → G'
  41. Polygon(N'', H', G') → poly5', g', n'', h'
  42. Vector(M', N'_1) → w
  43. Translate(F, w) → F'
  44. Translate(E, w) → E'
  45. Translate(M', w) → M''
  46. Polygon(F', E', M'') → poly10', m'', f', e'
  47. Vector(M, N'') → u_1
  48. Translate(M, u_1) → M'_1
  49. Translate(D, u_1) → D'_1
  50. Translate(A, u_1) → A'_1
  51. Polygon(M'_1, D'_1, A'_1) → poly11', a'_2, m'_2, d'_1
  52. Circle(A', Segment[F, M]) → c_1
  53. Circle(I, Segment[F, M]) → k_1
  54. Intersect(c_1, d, 1) → Q
  55. Intersect(k_1, p, 1) → R
  56. Polygon(I, R, D') → poly12, d'_2, i_1, r_1
  57. Polygon(Q, A', G') → poly13, g'_1, q_1, a'_3
  58. Polygon(D', R, J) → poly14, j_1, d'_3, r_2
  59. Polygon(G', Q, A) → poly15, a_4, g'_2, q_2

AI Drawing Prompt Reference

Draw a right triangle ABC with C as the right angle. Use C as the center to draw arcs with A and B as endpoints, intersecting at point D. Connect AD and reflect AD over C to get A'D'. Starting from D, draw vectors u and v, and use them to construct polygons and apply transformations to demonstrate the Pythagorean theorem geometrically.
The prompt above was compiled from the original drawing commands and is for reference only.