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Pythagorean Theorem Demonstration by Mark Beckwith

Pythagorean Theorem Demonstration by Mark Beckwith
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2016-07-09 04:57
TriangleGeometric Construction
This example visually demonstrates the Pythagorean theorem by dragging points and using a slider, illustrating the relationship between the sides of a right triangle. Core mathematical concepts include the Pythagorean theorem, right triangles, and distance calculations. It utilizes GeoGebra commands/objects such as Point, Intersect, CircleArc, Polygon, If, Rotate, Dilate, Vector, Translate, and Midpoint. Suitable for middle school students and above to learn and understand the proof and applications of the Pythagorean theorem.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. CircleArc(B, D, A) → c
  4. Point(c) → E
  5. Polygon(A, E, 4) → poly1, a, b, d, e, F, G
  6. Polygon(E, C, 4) → poly2, f, g, h, i, H, I
  7. Polygon(A, C, 4) → poly3, j, k, l, m, J, K
  8. Intersect(b, m) → L
  9. Intersect(i, l) → M
  10. Polygon(A, G, F, L) → poly4, a_1, g_1, f_1, l_1
  11. Polygon(M, I, J) → poly5, j_1, m_1, i_1
  12. Polygon(J, C, H) → poly6, h_1, j_2, c_1
  13. Polygon(A, E, L) → poly7, l_2, a_2, e_1
  14. Polygon(E, M, J, C) → poly8, e_2, m_2, j_3, c_2
  15. If(n < 1, n, 1) → r1
  16. Rotate(A, (-(((r1 * 90))°)), A) → A'
  17. Rotate(G, (-(((r1 * 90))°)), A) → G'
  18. Rotate(F, (-(((r1 * 90))°)), A) → F'
  19. Rotate(L, (-(((r1 * 90))°)), A) → L'
  20. Polygon(A', G', F', L') → poly4', a', g', f', l'
  21. Dilate(J, If[1 ≤ n < 2, 2 - n, If[n ≥ 2, 0, 1]], C) → J'
  22. Vector(J, J') → u
  23. Translate(M, u) → M'
  24. Translate(I, u) → I'
  25. Translate(J, u) → J'_1
  26. Polygon(M', I', J'_1) → poly5', j'_1, m', i'
  27. Midpoint(A, J) → N
  28. Vector(A, L) → v
  29. Translate(C, v) → C'
  30. Vector(A, E) → w
  31. Translate(C, w) → C'_1
  32. Polygon(C, C', C'_1) → poly9, c'_1, c_3, c'
  33. Polygon(C', J, H, C'_1) → poly10, c'_2, j_4, h_2, c'_3
  34. Dilate(J, If[2 ≤ n < 3, 3 - n, If[n ≥ 3, 0, 1]], K) → J'_2
  35. Vector(J, J'_2) → p
  36. Translate(C', p) → C''
  37. Translate(J, p) → J'_3
  38. Translate(H, p) → H'
  39. Translate(C'_1, p) → O
  40. Polygon(C'', J'_3, H', O) → poly10', c'', j'_3, h', o
  41. If(3 ≤ n ≤ 4, n - 3, 0) → r2
  42. Rotate(C, (-(((r2 * 90))°)), J) → C'_2
  43. Rotate(C', (-(((r2 * 90))°)), J) → C''_1
  44. Rotate(C'_1, (-(((r2 * 90))°)), J) → P
  45. Polygon(C'_2, C''_1, P) → poly9', p_1, c'_4, c''_1