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Pythagoras' Theorem -- Rectangle and Parallelogram

Pythagoras' Theorem -- Rectangle and Parallelogram
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2017-12-11 15:52
PolygonAngleVectorTransformationGeometric Construction
In collections Mathematics Form 1
This example demonstrates Pythagoras' Theorem in rectangles and parallelograms. Key mathematical concepts include Pythagoras' Theorem, properties of rectangles and parallelograms. Using GeoGebra commands such as If, Segment, Point, etc., the construction of rectangles and parallelograms is shown, along with transformations like rotation and translation to illustrate the theorem. Suitable for middle and high school students learning geometric construction and Pythagoras' Theorem.

GeoGebra Commands & Parameters

  1. If(b > 1, 1, b) → b_1
  2. Segment(A, B) → f
  3. Semicircle(A, B) → c
  4. Point(c) → C
  5. Rotate(C, (-(90°)), B) → C'_1
  6. Rotate(B, (-(90°)), C'_1) → B'
  7. OrthogonalLine(C, f) → t
  8. Rotate(C, 90°, A) → C'
  9. Rotate(A, 90°, C') → A'
  10. Line(C', A') → s
  11. Intersect(s, t) → D
  12. Vector(B', D) → v
  13. If(a > 1, 1, a) → a_1
  14. Vector(A', D) → u
  15. Segment(A, C) → g
  16. Segment(C, B) → h
  17. Segment(C, A') → i
  18. Segment(A', C') → j
  19. Segment(C', A) → k
  20. Segment(C, B') → l
  21. Segment(B', C'_1) → m
  22. Segment(C'_1, B) → n
  23. Rotate(A, 90°, B) → A'_1
  24. Rotate(B, 90°, A'_1) → B'_1
  25. Segment(A, B'_1) → p
  26. Segment(B'_1, A'_1) → q
  27. Segment(A'_1, B) → r
  28. Translate(C', Vector[(a_1 * u)]) → C''
  29. Translate(A', Vector[(a_1 * u)]) → A''
  30. Polygon(C'', A, C, A'') → poly1, c_3, d_1, c_1, d_2
  31. Line(B', C'_1) → d
  32. Translate(C'_1, Vector[(b_1 * v)]) → E
  33. Translate(B', Vector[(b_1 * v)]) → B''
  34. Polygon(B'', C, B, E) → poly2, e_1, c_2, e_2, e
  35. If(a < 1, 0, a > 2, 1, a - 1) → a_2
  36. If(b < 1, 0, b > 2, 1, b - 1) → b_2
  37. If(a < 2.5, 0, a - 2.5) → a_3
  38. If(b < 2.5, 0, b - 2.5) → b_3
  39. Intersect(t, f) → F
  40. Vector(C, F) → w
  41. Translate(C, Vector[(a_2 * w)]) → C'_2
  42. Translate(A'', Vector[(a_2 * w)]) → A'''
  43. Polygon(C'', A''', C'_2, A) → poly3, c'', a''', c'_2, a_4
  44. Vector(A, B'_1) → u_1
  45. Translate(C'', Vector[(a_3 * u_1)]) → C'''
  46. Translate(A''', Vector[(a_3 * u_1)]) → G
  47. Translate(C'_2, Vector[(a_3 * u_1)]) → H
  48. Translate(A, Vector[(a_3 * u_1)]) → A'_2
  49. Polygon(C''', G, H, A'_2) → poly3', c''', g_1, h_1, a'_2
  50. Translate(B'', Vector[(b_2 * w)]) → B'''
  51. Translate(C, Vector[(b_2 * w)]) → C'_3
  52. Polygon(B''', E, B, C'_3) → poly4, b''', e_3, b_4, c'_3
  53. Translate(B''', Vector[(b_3 * u_1)]) → I
  54. Translate(E, Vector[(b_3 * u_1)]) → E'
  55. Translate(B, Vector[(b_3 * u_1)]) → B'_2
  56. Translate(C'_3, Vector[(b_3 * u_1)]) → J
  57. Polygon(I, E', B'_2, J) → poly4', i_1, e', b'_2, j_1
  58. Angle(A, C, B) → α
  59. Polygon(A, B, C) → poly5, c_4, a_5, b_5
  60. SelectedIndex(Bahasa) → nn

AI Drawing Prompt Reference

Draw a semicircle with a diameter segment, place a point on the arc, and form a right triangle. Construct squares outward on each of the three sides. For the square on the hypotenuse, use rotations and translations to create parallelograms and rectangles that visually demonstrate the area relationship. Include sliders to control the shifting of parts, showing the Pythagorean theorem dynamically. The final figure shows a right triangle, three squares, several parallelograms, and auxiliary lines in a symmetric layout.
The prompt above was compiled from the original drawing commands and is for reference only.