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Dynamic Geometry Proof

Dynamic Geometry Proof
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2015-02-05 09:13
VectorCoordinate GeometryGeometric Construction
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This example demonstrates the properties of a parallelogram by dragging points and a slider. Core math concepts include parallelogram, Pythagorean theorem, normal distribution, probability, logarithmic functions, centroid, expected value, etc. Construction highlights the use of GeoGebra commands/objects like Point, Intersect, CircleArc, Segment, Line, Vector, Translate, Polygon, Dilate. Suitable for high school and above students to explore geometric properties and probability statistics.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. CircleArc(B, D, A) → c
  4. Point(c) → E
  5. Segment(A, E) → a
  6. Segment(E, F) → b
  7. Segment(C, E) → d
  8. Segment(E, G) → e
  9. Line(F, a) → f
  10. Line(G, d) → g
  11. Intersect(f, g) → H
  12. Segment(A, C) → h
  13. Line(H, E) → i
  14. Intersect(i, h) → I
  15. Line(A, i) → j
  16. Line(C, i) → k
  17. Vector(H, E) → u
  18. Translate(I, u) → I'
  19. Line(I', h) → l
  20. Intersect(j, l) → J
  21. Intersect(k, l) → K
  22. Vector(E, A) → v
  23. Vector(E, C) → w
  24. Translate(G, w) → G'
  25. Translate(F, v) → F'
  26. Polygon(A, E, F, F') → poly1, a_1, e_1, f_1, f'
  27. Polygon(A, J, K, C) → poly2, a_2, j_1, k_1, c_1
  28. Polygon(E, G, G', C) → poly3, e_2, g_1, g', c_2
  29. Dilate(F, If[m < 1, 1 - m, 0], H) → F'_1
  30. Dilate(G, If[m < 1, 1 - m, 0], H) → G'_1
  31. Translate(F'_1, v) → L
  32. Translate(G'_1, w) → M
  33. Polygon(A, L, F'_1, E) → poly4, a_3, l_1, f'_1, e_3
  34. Polygon(E, G'_1, M, C) → poly5, e_4, g'_1, m_1, c_3
  35. Vector(E, I) → n
  36. Translate(H, n) → H'
  37. Dilate(H, If[1 ≤ m < 2, 2 - m, 0], H') → H'_1
  38. Vector(L, A) → p
  39. Translate(H'_1, p) → N
  40. Polygon(L, H'_1, N, A) → poly6, l_2, h'_1, n_1, a_4
  41. Polygon(H'_1, M, C, N) → poly7, h'_2, m_2, c_4, n_2
  42. Dilate(I, If[2 ≤ m < 3, 3 - m, 0], I') → I'_1
  43. Vector(A, L) → q
  44. Translate(I'_1, q) → O
  45. Vector(I, A) → r
  46. Translate(O, r) → O'
  47. Translate(I'_1, r) → P
  48. Vector(I, C) → s
  49. Translate(O, s) → O'_1
  50. Translate(I'_1, s) → Q
  51. Polygon(O, O', P, I'_1) → poly8, o, o', p_1, i'_1
  52. Polygon(O, O'_1, Q, I'_1) → poly9, o_1, o'_1, q_1, i'_2

AI Drawing Prompt Reference

Draw a dynamic parallelogram demonstrating its properties by dragging points and a slider. Include coordinate axes, intersecting points, circle arcs, line segments, and vectors. Construct a pair of opposite sides, then use vector translation and dilation to create new shapes, forming nested polygons to illustrate geometric properties and probability statistics.
The prompt above was compiled from the original drawing commands and is for reference only.