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Proof Without Words: Pythagorean Theorem by Steve Phelps (6)

Proof Without Words: Pythagorean Theorem by Steve Phelps (6)
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2015-02-05 01:42
TriangleCoordinate GeometrySlider Animation
In collections Geometry Review Similarity & Right Triangle Trigonometry Similarity, Right Triangles, and Trigonometry (SRT) Cluster Proofs Without Words Proofs Without Words
This example demonstrates the Pythagorean Theorem through dragging points and sliders. It involves the core mathematical concept of the Pythagorean Theorem. Using GeoGebra commands such as Point, Intersect, Mirror, CircleArc, Polygon, etc., a dynamic geometric figure is constructed to help students understand the geometric meaning of the theorem. Suitable for middle school and above students learning geometric proofs.

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 point A on the x-axis, point B at the origin, and point C on the y-axis. Use dragging points and sliders to construct a dynamic geometric figure demonstrating the relationship between the sides of triangle ABC. Utilize tools like mirroring, circular arcs, and polygons to create auxiliary lines and triangles, and finally, through scaling and moving, show the geometric proof of the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.