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Measuring Angles

Measuring Angles
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2023-12-20 17:31
AngleCoordinate GeometryGeometric Construction
In collections Wiederholung Winkel: Bezeichnung, Arten, Messen & Zeichnen
This example demonstrates how to use GeoGebra to measure angles. It involves the core mathematical concepts of angle definition, angle measurement, and relationships between angles. The construction points include using the UnicodeToText command to convert Unicode characters to text, using the Point command to create points, using the Sequence command to create sequences, and so on. It is suitable for middle school mathematics, geometry, and measurement education.

GeoGebra Commands & Parameters

  1. UnicodeToText(Remove[TextToUnicode[input1], Sequence[32, m, 1, 100]]) → input1clean
  2. Point(Segment[StartLineal2, T]) → PLineal2
  3. Sequence(((sizecircle * cos(m°)) + x(PLineal2), (sizecircle * sin(m°)) + y(PLineal2)), m, 0, 360, 5) → listcirclepoints2
  4. Point(listcirclepoints2) → DLineal2
  5. Point(Segment[StartLineal, S]) → PLineal
  6. Sequence(((sizecircle * cos(m°)) + x(PLineal), (sizecircle * sin(m°)) + y(PLineal)), m, -15, 210, 5) → listcirclepoints
  7. Point(listcirclepoints) → DLineal
  8. If(selected2 ≟ 1, spitz1, stumpf1) → correct3
  9. If(selected2 ≟ 1, stumpf2, spitz2) → correct5
  10. UnicodeToText(Remove[TextToUnicode[input2], Sequence[32, m, 1, 100]]) → input2clean
  11. Join(Sequence[Shuffle[{50, 60, 70}], i, 1, 40]) → listwinkel1
  12. If(selected2 ≟ 1, Text[winkel1], Text[180° - winkel1]) → winkel1check
  13. If(selected2 ≟ 2, Text[winkel1], Text[180° - winkel1]) → winkel2check
  14. Text(winkel2) → winkel10check
  15. UnicodeToText(Remove[TextToUnicode[input10], Sequence[32, m, 1, 100]]) → input10clean
  16. UnicodeToText(Remove[TextToUnicode[input11], Sequence[32, m, 1, 100]]) → input11clean
  17. Rotate(S + (2.6, 0), winkel1, S) → PLupe
  18. Point(Line[S, xAxis]) → S1
  19. Segment(S1, S + Vector[S1, S]) → f
  20. Rotate(S + (5, 0), winkel1, S) → W
  21. Segment(S, W) → g
  22. Angle(S2, S, W) → α
  23. Angle(S2, S, W) → alp
  24. Angle(W, S, S1) → bet
  25. Point(Line[A1, xAxis]) → A2
  26. Rotate(Segment[S + (2.5, 0), S + (3.1, 0)], winkel1, S) → h
  27. Rotate(T + (5.2, 0), 360° - winkel2, T) → T2
  28. Segment(T, T1) → i
  29. Segment(T, T2) → j
  30. Angle(T1, T, T2) → alp2
  31. Angle(T2, T, T1) → bet2
  32. Rotate(DLineal2, 90°, PLineal2) → Lineal3
  33. Rotate(DLineal2, -90°, PLineal2) → Lineal4
  34. IndexOf(DLineal2, listcirclepoints2) → a
  35. Textfield(input10) → Eingabefeld10
  36. Rotate(T + (2.6, 0), 360° - winkel2, T) → PLupe2
  37. Rotate(Segment[T + (2.5, 0), T + (3.1, 0)], 360° - winkel2, T) → h2
  38. Textfield(input11) → Eingabefeld11
  39. Point(Line[A3, yAxis]) → A4
  40. Point(Line[A, xAxis]) → B
  41. SpeechBubbleLeft(E, 9.95, 2.15) → Vieleck1
  42. SpeechBubbleLeft(C, 8, 2.8) → Vieleck2
  43. SpeechBubbleLeft(C, 5.2, 1.7) → Vieleck3
  44. SpeechBubbleLeft(C, 9.6, 2.25) → Vieleck4
  45. SpeechBubbleLeft(M, 4.3, 1.7) → Vieleck5
  46. Rotate(DLineal, 90°, PLineal) → Lineal1
  47. Rotate(DLineal, -90°, PLineal) → Lineal2
  48. Textfield(input1) → Eingabefeld1
  49. Textfield(input2) → Eingabefeld2
  50. Textfield(input12) → Eingabefeld12
  51. Text(input12) → input12text

AI Drawing Prompt Reference

In a Cartesian plane with a horizontal axis, draw two angle diagrams sharing the same measurement context: create an initial ray and another ray rotated from it to form two angles, labeled α and β, with their openings measured relative to the horizontal reference. Add a circular set of points along a circle to represent an angle-measuring scale, then place the rays so they intersect the scale. Display angle text for the computed angles, and include two input fields at the bottom for entering the angle values to verify, with the corresponding angle readouts shown on the figure.
The prompt above was compiled from the original drawing commands and is for reference only.