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Pythagorean Theorem Proof Without Words by Steve Phelps (2)

Pythagorean Theorem Proof Without Words by Steve Phelps (2)
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2019-06-06 01:11
TriangleVectorTrigonometry
This example demonstrates the Pythagorean theorem for any triangle through geometric transformations. It uses concepts like vectors, polygons, and geometric transformations. By constructing semicircles, lines, angles, and polygons, it provides a visual proof of the theorem. Suitable for students in middle school and above for learning geometric proofs.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Point(xAxis) → A
  3. Semicircle(A, B) → c
  4. Point(c) → C
  5. Segment(A, C) → g
  6. Segment(C, B) → h
  7. Segment(B, A) → i
  8. Angle(A, C, B) → α
  9. Polygon(C, D, B) → t1, b, c_1, d
  10. Polygon(A, E, C) → t2, c_2, a, e
  11. Line(D, h) → f
  12. Line(E, g) → j
  13. Intersect(f, j) → F
  14. Line(F, C) → k
  15. Intersect(k, i) → G
  16. Vector(F, C) → u
  17. Translate(G, u) → G'
  18. Line(G', i) → l
  19. Point(l) → H
  20. Polygon(A, H, B) → t3, b_1, a_1, h_1
  21. If(0 < o ≤ 1, Polygon[Dilate[E, 1 - o, F], A, C], Polygon[F, A, C]) → t4
  22. If(2 < o ≤ 3, Polygon[A, Dilate[C, 3 - o, G'], Dilate[F, 3 - o, G]], Polygon[A, G, G']) → t5
  23. If(4 < o ≤ 5, Polygon[Dilate[D, 5 - o, F], B, C], Polygon[F, B, C]) → t6
  24. If(6 < o ≤ 7, Polygon[B, Dilate[C, 7 - o, G'], Dilate[F, 7 - o, G]], Polygon[B, G, G']) → t7
  25. If(8 < o ≤ 9, Polygon[G, B, Dilate[G', 9 - o, H]], Polygon[G, B, H]) → t8
  26. If(8 < o ≤ 9, Polygon[G, A, Dilate[G', 9 - o, H]], Polygon[G, A, H]) → t9

AI Drawing Prompt Reference

Draw a right triangle ABC with AB as the hypotenuse. Construct a semicircle with AB as the diameter, and draw line segments g and h connecting A to C and B to C, respectively. Use rotations and translations to construct a series of similar triangles and quadrilaterals, ultimately forming a visually proof of the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.