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Constructing and Identifying Right and Supplementary Angles

Constructing and Identifying Right and Supplementary Angles
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2024-04-04 21:03
AngleTrigonometryGeometric Construction
In collections Besondere Winkelpaare
This example demonstrates how to construct right angles and supplementary angles. Key math concepts include angle classification (acute, right, obtuse), angle measurement, and relationships between orthogonal and supplementary angles. GeoGebra commands like Polygon, PointIn, Segment, OrthogonalLine, Rotate are used for drawing and transforming angles. Suitable for upper elementary students for geometry construction practice and angle understanding.

GeoGebra Commands & Parameters

  1. SpeechBubbleLeft(PBubbleAlex, 10.5, 1.3) → bubble1
  2. Polygon(Q1, Q2, Q3, Q4) → q1, i_1, j_1, k_1, l
  3. PointIn(q1) → arrowCirclePoint_1
  4. Segment(arrowCircleMidpoint, arrowCirclePoint_1) → f
  5. OrthogonalLine(C, f) → g
  6. Point(g) → D
  7. Segment(D, C) → h
  8. PointIn(q1) → arrowCirclePoint
  9. Segment(arrowCircleMidpoint, arrowCirclePoint) → i
  10. OrthogonalLine(C, i) → j
  11. Point(j) → F
  12. Segment(F, C) → k
  13. Intersect(f, h) → Schnittpunkt1
  14. Intersect(i, k) → Schnittpunkt2
  15. Angle(arrowCirclePoint_1, Schnittpunkt1, D) → γ
  16. Angle(arrowCirclePoint, Schnittpunkt2, F) → δ
  17. Angle(arrowCirclePoint, arrowCircleMidpoint, arrowCirclePoint_1) → α
  18. Angle(F, C, D) → α_1
  19. Textfield(input1) → InputBox1
  20. SelectedIndex(dropdown) → index
  21. SpeechBubbleLeft(PBubbleAlex - (0, 0.1), 8.3, 1.8) → bubble2
  22. Line(arrowCircleMidpoint, arrowCirclePoint) → m
  23. Line(arrowCircleMidpoint, arrowCirclePoint_1) → n
  24. Point(n) → G
  25. Segment(arrowCirclePoint_1, G) → p
  26. Point(m) → H
  27. Segment(arrowCirclePoint, H) → q
  28. SpeechBubbleLeft(PBubbleElia, 7, 1.2) → bubble3
  29. Polygon(P1, P2, P3, P4) → p2, t_1, u, v, w
  30. PointIn(p2) → A
  31. Segment(I, A) → r
  32. Polygon(P1_{1}, P2_{1}, P3_{1}, P4_{1}) → p2_{1}, t_{2}, u_{1}, v_{1}, w_{1}
  33. PointIn(p2_{1}) → K
  34. Segment(I, K) → s
  35. Angle(K, I, A) → β
  36. Point(r) → L
  37. OrthogonalLine(L, s) → t
  38. Point(t) → M
  39. Point(t) → N
  40. Segment(M, N) → a
  41. Intersect(s, a) → O
  42. Angle(L, O, I) → ε
  43. OrthogonalLine(P, r) → b
  44. Point(b) → Q
  45. Segment(Q, P) → c
  46. Intersect(r, c) → R
  47. Angle(I, R, P) → ζ
  48. Intersect(a, c) → S
  49. Segment(M, S) → d
  50. Segment(Q, S) → e
  51. Angle(R, S, O) → η
  52. SelectedIndex(dropdown1) → index2
  53. SpeechBubbleLeft(PBubbleElia + (0.2, -0.5), 7.8, 1.3) → bubble5
  54. Textfield(input2) → InputBox2
  55. Textfield(input3) → InputBox3
  56. Ray(I, A) → f_1
  57. Point(f_1) → T
  58. Segment(A, T) → g_1
  59. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint_1] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] + arrowCircleDistance + arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint_1] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] + arrowCircleDistance + arrowCircleAngle))) + (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint_1] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] + arrowCircleDistance + arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] + arrowCircleDistance + arrowCircleAngle)))]])) → arrowCircleArrow01_1
  60. Segment(arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint_1] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] - arrowCircleDistance - arrowCircleAngle))), arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint_1] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] - arrowCircleDistance - arrowCircleAngle))) - (arrowCircleLength * UnitOrthogonalVector[Vector[arrowCircleMidpoint, arrowCircleMidpoint + (Distance[arrowCircleMidpoint, arrowCirclePoint_1] * (cos(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] - arrowCircleDistance - arrowCircleAngle), sin(Angle[arrowCircleMidpoint + (1, 0), arrowCircleMidpoint, arrowCirclePoint_1] - arrowCircleDistance - arrowCircleAngle)))]])) → arrowCircleArrow02_1
  61. 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)))]])) → arrowCircleArrow02
  62. 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)))]])) → arrowCircleArrow01
  63. Ray(I, K) → h_1
  64. Point(h_1) → A_1
  65. Segment(K, A_1) → l_1
  66. PointIn(p2_{1}) → J_{1}
  67. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((1 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow1
  68. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((2 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow2
  69. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((3 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow3
  70. Rotate(Segment[ArrowCenter + (ArrowDistance, 0), ArrowCenter + (ArrowDistance + ArrowLength, 0)], ArrowAngle + ((4 - 1) * (360°) / ArrowNumber), ArrowCenter) → arrow4
  71. SpeechBubbleLeft(PBubbleElia + (0.2, 0), 7.8, 1) → bubble4

AI Drawing Prompt Reference

Draw two quadrilaterals for angle demonstration. In the first quadrilateral, draw two line segments from an interior point to one side, with a fixed point on that side as foot, construct perpendicular lines to these two segments forming four intersection points, and measure the four angles formed at these intersections including acute, right and obtuse angles; also connect two interior points to a fixed point. In the second quadrilateral, draw two line segments from a fixed point I into the interior, take a point on one segment to construct a perpendicular line intersecting the other segment forming an intersection point and measure the angle; take a point on the first segment to construct a perpendicular line intersecting the other segment and measure another angle. Add speech bubble annotations outside the quadrilaterals.
The prompt above was compiled from the original drawing commands and is for reference only.