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Supplementary and Adjacent Angles

Supplementary and Adjacent Angles
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2024-02-13 21:29
AngleTransformationGeometric ConstructionSlider Animation
In collections Besondere Winkelpaare
This example demonstrates the geometric relationship between supplementary and adjacent angles. Key math concepts include the definition of supplementary angles (sum of two angles is 180°), the definition of adjacent angles (share a vertex and one side), and angle size comparison. GeoGebra commands/objects used in construction: SpeechBubbleLeft, Circle, Point, Segment, OrthogonalLine, Intersect, Mirror, Arc, Angle, Vector, Rotate, Translate, SelectedIndex, CircleArc, Textfield. Suitable for 5-6th grade students to learn and understand angle classification, supplementary angles, and adjacent angles.

GeoGebra Commands & Parameters

  1. SpeechBubbleLeft(PBubble - (0, 1), 12.4, 2.9) → poly1
  2. SpeechBubbleLeft(PBubble + (0, 0.55), 11, 1.3) → poly2
  3. SpeechBubbleLeft(PBubble, 5, 1) → poly3
  4. Circle(A, 3.4) → c
  5. Point(c) → B
  6. Segment(A, B) → s11
  7. OrthogonalLine(A, s11) → perpLine
  8. Intersect(c, perpLine, 2) → MCOM
  9. Mirror(B, A) → MSUP
  10. Arc(c, B, MSUP) → supplArc
  11. Point(supplArc) → B'
  12. Angle(B, A, B') → α
  13. Segment(A, B') → s12
  14. Circle(A, 2.3) → cExt
  15. Mirror(B, cExt) → B'_{2}
  16. Segment(B, B'_{2}) → sv11
  17. Mirror(B', cExt) → B''_{1}
  18. Segment(B', B''_{1}) → sv12
  19. Vector(C, V) → u
  20. Rotate(D, 180° - α, C) → D'
  21. Segment(C, D) → s21
  22. Segment(C, D') → s22
  23. Vector(A, V) → v
  24. Translate(A, Vector[(transSli1 * v)]) → A'
  25. Translate(D', Vector[(transSli2 * u)]) → D''
  26. Translate(B, Vector[(transSli1 * v)]) → B'_{1}
  27. Angle(D'', V, B'_{1}) → ang
  28. Rotate(A', (rotAng * rotSli), V) → A''
  29. Translate(A, Vector[(transSli1 * v)]) → A'_{1}
  30. Translate(B', Vector[(transSli1 * v)]) → B''
  31. Rotate(B'', (rotAng * rotSli), V) → B'''
  32. Translate(B', Vector[(transSli1 * u)]) → B''_{2}
  33. Translate(B', Vector[(transSli1 * v)]) → B''_{3}
  34. Translate(B, Vector[(transSli1 * u)]) → B'_{3}
  35. Translate(B, Vector[(transSli1 * v)]) → B'_4
  36. Rotate(B, α - 15°, A) → BF
  37. Translate(C, u) → C'
  38. Translate(C, u) → C'_{1}
  39. Translate(C, Vector[(transSli2 * u)]) → C'_{2}
  40. Translate(C, Vector[(transSli2 * u)]) → C'_{3}
  41. Translate(D, Vector[(transSli2 * u)]) → D'_{1}
  42. Point(s11) → E
  43. Point(s21) → F
  44. Rotate(A'_{1}, (rotAng * rotSli), V) → G
  45. Rotate(B'_{1}, (rotAng * rotSli), V) → H
  46. Rotate(B'_4, (rotAng * rotSli), V) → S
  47. Rotate(B''_{3}, (rotAng * rotSli), V) → T
  48. Segment(G, H) → s11''
  49. Segment(A'', B''') → s12''
  50. Segment(C'_{2}, D'_{1}) → s21'
  51. Segment(C'_{3}, D'') → s22'
  52. Angle(D'_{1}, C'_{2}, D'') → β
  53. Angle(H, A', B''') → α'
  54. Angle(D'_{1} + (2, 0), A', B''' - (2, 0)) → γ
  55. SelectedIndex(dropdown) → index
  56. CircleArc(A', D'_{1} - (0.4, 0), B''') → d
  57. Point(d) → arrowCirclePoint
  58. Segment(A', arrowCirclePoint) → seg
  59. CircleArc(A', D'_{1} - (0.23, 0), B''') → e
  60. Mirror(arrowCirclePoint, e) → I'
  61. Segment(arrowCirclePoint, I') → seg2
  62. Angle(I', A', B''') → α''
  63. Angle(D'_{1}, A', I') → β'
  64. SpeechBubbleLeft(PBubble, 12.4, 1.9) → poly1_1
  65. Textfield(input1) → InputBox1
  66. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle))) + (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] + arrowCircleDistance + arrowCircleAngle)))]])) → f
  67. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle))) - (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint] - arrowCircleDistance - arrowCircleAngle)))]])) → g

AI Drawing Prompt Reference

Create a geometric figure showing supplementary and adjacent angles: Draw a large circle and pick a point on it as the vertex, draw a line segment from the vertex to another point on the circle, then draw a perpendicular line through the vertex to intersect the circle at another point. Mirror the second point on the circle across the vertex to create a supplementary angle, draw the arc between these points and mark the angle. Inside the large circle, draw a smaller concentric circle and mirror points on the large circle across the small circle to create corresponding points. Translate some points using vectors and rotate certain points, then connect relevant points with line segments to demonstrate various positional relationships of supplementary and adjacent angles. Include multiple speech bubbles to label angle information and explanatory text.
The prompt above was compiled from the original drawing commands and is for reference only.