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Pythagorean Theorem Interactive Demo

Pythagorean Theorem Interactive Demo
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2016-07-09 04:45
TriangleGeometric Construction
In collections Algebra 1
This example dynamically demonstrates the Pythagorean Theorem in right-angled triangles by dragging points and a slider. It involves core concepts like the Pythagorean Theorem, right triangles, and distance formulas. Constructed using commands such as Point, Intersect, Mirror, CircleArc, Polygon, Ray, If, Dilate, Vector, Translate, and Segment in GeoGebra. Ideal for middle school and above to understand proof and application, enhancing spatial reasoning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. Mirror(A, B) → A'
  4. CircleArc(B, C, A) → c
  5. Point(c) → D
  6. Polygon(A, D, 4) → poly1, a, b, d, e, E, F
  7. Polygon(D, A', 4) → poly2, f, g, h, i, G, H
  8. Polygon(A', A, 4) → poly3, j, k, l, m, I, J
  9. Ray(F, E) → n
  10. Ray(G, H) → p
  11. Intersect(n, p) → K
  12. Ray(K, D) → q
  13. If(0 ≤ o < 1, 1 - o, 0) → scale1
  14. Dilate(E, scale1, K) → E'
  15. Dilate(H, scale1, K) → H'
  16. Vector(E, F) → u
  17. Vector(H, G) → v
  18. Translate(E', u) → E''
  19. Translate(H', v) → H''
  20. Polygon(E', D, A, E'') → poly4, e', d_1, a_1, e''
  21. Polygon(A', H'', H', D) → poly5, a', h'', h', d_2
  22. If(1 ≤ o < 2, 2 - o, 1) → scale2
  23. Dilate(K, scale2, D) → K'
  24. Vector(K, K') → w
  25. Translate(E', w) → E''_1
  26. Translate(D, w) → D'
  27. Translate(A, w) → A'_1
  28. Translate(E'', w) → E'''
  29. Polygon(E''_1, D', A'_1, E''') → poly4', e''_1, d', a'_1, e'''
  30. Translate(A', w) → A''
  31. Translate(H'', w) → H'''
  32. Translate(H', w) → H''_1
  33. Translate(D, w) → D'_1
  34. Polygon(A'', H''', H''_1, D'_1) → poly5', a'', h''', h''_1, d'_1
  35. Intersect(j, q) → L
  36. If(2 ≤ o ≤ 3, 3 - o, 1) → scale3
  37. Dilate(D, scale3, L) → D'_2
  38. Vector(A, I) → r
  39. Translate(D'_2, r) → M
  40. Polygon(I, A, D'_2, M) → poly6, i_1, a_2, d'_2, m_1
  41. Polygon(D'_2, A', J, M) → poly7, d'_3, a'_2, j_1, m_2
  42. Segment(E, K) → s
  43. Segment(K, H) → t
  44. Ray(K, L) → b_1
  45. Intersect(l, b_1) → N
  46. Segment(K, N) → c_1

AI Drawing Prompt Reference

Draw a right triangle ABC with A on the x-axis, B at the origin, and C on the y-axis. Dynamically demonstrate the Pythagorean Theorem by dragging points and using a slider. Construct a circular arc with B as the center and BC as the radius, and connect A and D to form a polygon. Then construct another circular arc with A' as the center and A'D as the radius, and connect D and A' to form another polygon. Finally, use scaling and translation to construct multiple polygons and segments, illustrating the proof of the Pythagorean Theorem.
The prompt above was compiled from the original drawing commands and is for reference only.