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Geometric Proof of Pythagorean Theorem by Steve Phelps (3)

Geometric Proof of Pythagorean Theorem by Steve Phelps (3)
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2019-06-06 20:58
TrianglePolygonVectorGeometric Construction
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This example dynamically demonstrates the relationship between arbitrary triangles and parallelograms in the Pythagorean Theorem. It involves core math concepts like the Pythagorean Theorem, triangles, parallelograms, vectors, and transformations. The construction uses GeoGebra commands and objects such as Polygon, Line, Intersect, Vector, Translate, Point, Segment, and If. Suitable for high school mathematics teaching to visually understand the generality of the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Polygon(A, D, G, C) → q1, a_1, d, g, c_1
  3. Polygon(C, F, E, B) → q2, f, h, i, j
  4. Line(D, G) → k
  5. Line(F, E) → l
  6. Intersect(k, l) → H
  7. Line(H, C) → m
  8. Intersect(m, c) → I
  9. Vector(H, C) → u
  10. Translate(I, u) → I'
  11. Line(I', c) → n
  12. Point(n) → J
  13. Polygon(J, A, B, K) → q3, j_1, a_2, b_1, k_1
  14. Segment(H, C) → p
  15. Segment(I, I') → q
  16. If(0 < o ≤ 1, Polygon[A, C, Dilate[G, 1 - o, H], Dilate[G, 1 - o, H] + A - C], Polygon[A, C, H, H + A - C]) → q4
  17. If(2 < o ≤ 3, Polygon[A, Dilate[C, 3 - o, I], Dilate[C, 3 - o, I] + H - C, A + H - C], Polygon[A, I, I + H - C, A + H - C]) → q5
  18. If(4 < o ≤ 5, Polygon[Dilate[I, 5 - o, I'], Dilate[I, 5 - o, I'] + H - C, A + H - C + Dilate[I, 5 - o, I'] - I, A + Dilate[I, 5 - o, I'] - I], Polygon[A, I, I', A + I' - I]) → q6
  19. If(6 < o ≤ 7, Polygon[B, C, Dilate[F, 7 - o, H], Dilate[F, 7 - o, H] + E - F], Polygon[B, C, H, H + E - F]) → q7
  20. If(8 < o ≤ 9, Polygon[B + H - C, B, Dilate[C, 9 - o, I], Dilate[C, 9 - o, I] + H - C], Polygon[B, I, I + H - C, B + H - C]) → q8
  21. If(10 < o ≤ 11, Polygon[Dilate[I, 11 - o, I'], B + Dilate[I, 11 - o, I'] - I, B + Dilate[I, 11 - o, I'] - I + H - C, Dilate[I, 11 - o, I'] + H - C], Polygon[I', I, B, B + I' - I]) → q9
  22. If(12 < o ≤ 13, Polygon[I, B, Dilate[B + I' - I, 13 - o, K], Dilate[B + I' - I, 13 - o, K] + I - B], Polygon[I, B, K, K + I - B]) → q10
  23. If(12 < o ≤ 13, p) → r
  24. If(12 < o ≤ 13, Polygon[I, A, Dilate[A + I' - I, 13 - o, J], Dilate[A + I' - I, 13 - o, J] + I - A], Polygon[A, J, J + I - A, I]) → q11

AI Drawing Prompt Reference

Draw a right triangle ABC with AB and BC as the legs and AC as the hypotenuse. Construct a parallelogram with C as one vertex, then use translations and scalings to create a series of similar parallelograms, ultimately forming a triangle with vertices A, B, and C to demonstrate the dynamic proof of the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.