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Proof Without Words by Steve Phelps (11)

Proof Without Words by Steve Phelps (11)
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2015-02-05 06:51
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This example demonstrates the symmetry property of triangles by dragging points and sliders. It involves key mathematical concepts such as angles, vectors, and transformations. Using GeoGebra commands like Point, Intersect, Mirror, and Dilate, dynamic geometric figures are constructed. Suitable for middle school and above students to learn geometric transformations and 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, 3) → poly1, a, b, d, E
  7. Polygon(D, A', 3) → poly2, e, f, g, F
  8. Polygon(A', A, 3) → poly3, h, i, j, G
  9. Line(E, a) → k
  10. Line(F, e) → l
  11. Intersect(k, l) → K
  12. Line(K, D) → m
  13. Dilate(F, If[n < 1, 1 - n, 0], K) → F'
  14. Polygon(A', F', D) → poly4, d_1, a', f'
  15. Dilate(E, If[n < 1, 1 - n, 0], K) → E'
  16. Polygon(A, E', D) → poly5, d_2, a_1, e'
  17. Intersect(m, h) → H
  18. Dilate(D, If[1 ≤ n < 2, 2 - n, 0], H) → D'
  19. Vector(D, K) → u
  20. Translate(D', u) → D''
  21. Polygon(D'', A, D') → poly6, d', d'', a_2
  22. Polygon(D'', D', A') → poly7, a'_1, d''_1, d'_1
  23. Midpoint(h) → I
  24. Dilate(H, If[2 ≤ n ≤ 3, 3 - n, 1], I) → H'
  25. Line(G, h) → p
  26. Rotate(D'', (-((((n - 2) * 180))°)), I) → D'''
  27. Rotate(A, (-((((n - 2) * 180))°)), I) → A'_1
  28. Rotate(D', (-((((n - 2) * 180))°)), I) → D''_1
  29. Polygon(D''', A'_1, D''_1) → poly6', d''_2, d''', a'_2
  30. Rotate(D'', (-((((n - 2) * 180))°)), I) → D'''_1
  31. Rotate(D', (-((((n - 2) * 180))°)), I) → D''_2
  32. Rotate(A', (-((((n - 2) * 180))°)), I) → A''
  33. Polygon(D'''_1, D''_2, A'') → poly7', a'', d'''_1, d''_3

AI Drawing Prompt Reference

Draw triangle ABC, then mirror point A at point B to get A'. Construct a circular arc BCA and take point D on it. Draw triangle AD3 and A'D3. Draw lines ED and F', find their intersection K, then enlarge F' at K to get F'. Construct triangle A'F'D'. Enlarge E' at K to get E', then construct triangle ADE'. Find the midpoint I of DK, enlarge H at I to get H', draw line GH, and rotate D'', A'1, D''1, D''', A'', D'''1, D''2, A'' to form several triangles.
The prompt above was compiled from the original drawing commands and is for reference only.