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Special Parallel Angles

Special Parallel Angles
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2024-04-04 21:02
AngleTransformationGeometric Construction
In collections Besondere Winkelpaare
This example demonstrates the properties of special parallel angles, including corresponding angles and alternate interior angles. Key mathematical concepts include angle classification and measurement. Using GeoGebra commands such as Segment, Angle, and Translate, the construction involves parallel lines and angles. Suitable for 5-6 grade students learning geometry and angle-related knowledge.

GeoGebra Commands & Parameters

  1. SelectedIndex(DropDown1) → input1
  2. Point(Segment[G1, G1 + (3.7 * UnitVector[vG2])]) → G2
  3. Point(Line[G1 + (3, 1.5), xAxis]) → G3Start
  4. Point(Translate[Segment[(0, 0), (8, 0)], G1 + (1.5, y(G3Start) - y(G1))]) → G3
  5. Segment(H5, H6) → h3
  6. Segment(H2, H1 - (spaziGerade * UnitVector[Vector[H1, H2]])) → h1
  7. Intersect(h1, h3) → S3
  8. Angle(winkelPoints3(3), S3, winkelPoints3(2)) → alpha2
  9. If(IsInteger[numselected / 2], Sequence[2, 8, 2], Sequence[1, 7, 2]) → listCorrectNums
  10. Zip(¬(listSelected(m)), m, If[¬IsInteger[numselected / 2], Sequence[2, 8, 2], Sequence[1, 7, 2]]) → listCorrect2False
  11. Zip(listSelected(m), m, listCorrectNums) → listCorrect2Correct
  12. Textfield(input1) → Eingabefeld1
  13. Textfield(input2) → Eingabefeld2
  14. Translate(Segment[G1, G1 + (sizeGerade, 0)], ((-spaziGerade), 0)) → g1
  15. Point(Line[G1, vG2]) → G2Start
  16. Translate(Segment[G2, G2 + (sizeGerade, 0)], ((-spaziGerade), 0)) → g2
  17. PointIn(Circle[G1, 12]) → G4
  18. Translate(Segment[G3, G4 + (spaziGerade * UnitVector[Vector[G3, G4]])], Vector[((-spaziGerade) * UnitVector[Vector[G3, G4]])]) → g3
  19. Intersect(g1, g3) → S1
  20. Intersect(g2, g3) → S2
  21. Rotate(winkelPoints1(3), (-(drehung1°)), S1) → Drehpunkt1
  22. Rotate(winkelPoints2(3), (-(drehung2°)), S2) → Drehpunkt2
  23. CircleSector(S2, winkelPoints2(2), winkelPoints2(3)) → w5
  24. CircleSector(S2, winkelPoints2(3), winkelPoints2(1)) → w6
  25. CircleSector(S2, winkelPoints2(1), winkelPoints2(4)) → w7
  26. CircleSector(S2, winkelPoints2(4), winkelPoints2(2)) → w8
  27. CircleSector(S1, winkelPoints1(2), winkelPoints1(3)) → w1
  28. CircleSector(S1, winkelPoints1(3), winkelPoints1(1)) → w2
  29. CircleSector(S1, winkelPoints1(1), winkelPoints1(4)) → w3
  30. CircleSector(S1, winkelPoints1(4), winkelPoints1(2)) → w4
  31. CircleArc(S1, Drehpunkt1, Rotate[winkelPoints1(3), -0.1°, S1]) → kreis1
  32. CircleArc(S2, Drehpunkt2, Rotate[winkelPoints2(3), -0.1°, S2]) → kreis2
  33. Segment(G2 + (sizeGerade - spaziGerade, 0), G2 + (sizeGerade - spaziGerade - 3, 0)) → g2kurz
  34. Segment(G1 + (sizeGerade - spaziGerade, 0), G1 + (sizeGerade - spaziGerade - 4, 0)) → g1kurz
  35. Angle(winkelPoints1(2), S1, winkelPoints1(3)) → alpha1
  36. Angle(winkelPoints1(3), S1, winkelPoints1(1)) → beta1
  37. Angle(winkelPoints1(1), S1, winkelPoints1(4)) → gamma1
  38. Angle(winkelPoints1(4), S1, winkelPoints1(2)) → delta1
  39. Point(Line[Cora1, xAxis]) → Cora2
  40. Point(Line[SB3, yAxis]) → SB4
  41. Point(Line[Birne1, xAxis]) → Birne2
  42. Translate(h1, Vector[H1, H3]) → h2
  43. Intersect(h2, h3) → S4
  44. CircleSector(S3, winkelPoints3(3), winkelPoints3(2)) → v1
  45. CircleSector(S3, winkelPoints3(4), winkelPoints3(1)) → v2
  46. CircleSector(S4, winkelPoints4(4), winkelPoints4(1)) → v4
  47. CircleSector(S4, winkelPoints4(3), winkelPoints4(2)) → v3
  48. Textfield(input3) → Eingabefeld3
  49. Textfield(input4) → Eingabefeld4
  50. Sequence(Pos7 + (1, ((-m) * 1.05) - 1), m, 0, 2) → listPos7
  51. Segment(H1 - (spaziGerade * UnitVector[Vector[H1, H2]]), H1 + (spaziGerade * UnitVector[Vector[H1, H2]])) → h1kurz
  52. Translate(h1kurz, Vector[H1, H3]) → h2kurz
  53. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  54. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  55. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte, {{(-17.48600000000001, 11.44600000000002), (-16.383243107769434, 11.44600000000002), (-15.280486215538858, 11.44600000000002), (-14.17772932330828, 11.44600000000002), (-13.074972431077704, 11.44600000000002), (-11.972215538847127, 11.44600000000002), (-10.86945864661655, 11.44600000000002), (-9.766701754385974, 11.44600000000002), (-8.663944862155397, 11.44600000000002), (-7.56118796992482, 11.44600000000002), (-6.458431077694243, 11.44600000000002), (-5.355674185463666, 11.44600000000002), (-4.252917293233089, 11.44600000000002), (-3.1501604010025126, 11.44600000000002), (-2.0474035087719358, 11.44600000000002), (-0.944646616541359, 11.44600000000002), (0.15811027568921787, 11.44600000000002)}, {(-17.48600000000001, 10.34232107023413), (-16.383243107769434, 10.34232107023413), (-15.280486215538858, 10.34232107023413), (-14.17772932330828, 10.34232107023413), (-13.074972431077704, 10.34232107023413), (-11.972215538847127, 10.34232107023413), (-10.86945864661655, 10.34232107023413), (-9.766701754385974, 10.34232107023413), (-8.663944862155397, 10.34232107023413), (-7.56118796992482, 10.34232107023413), (-6.458431077694243, 10.34232107023413), (-5.355674185463666, 10.34232107023413), (-4.252917293233089, 10.34232107023413), (-3.1501604010025126, 10.34232107023413), (-2.0474035087719358, 10.34232107023413), (-0.944646616541359, 10.34232107023413), (0.15811027568921787, 10.34232107023413)}, {(-17.48600000000001, 9.238642140468242), (-16.383243107769434, 9.238642140468242), (-15.280486215538858, 9.238642140468242), (-14.17772932330828, 9.238642140468242), (-13.074972431077704, 9.238642140468242), (-11.972215538847127, 9.238642140468242), (-10.86945864661655, 9.238642140468242), (-9.766701754385974, 9.238642140468242), (-8.663944862155397, 9.238642140468242), (-7.56118796992482, 9.238642140468242), (-6.458431077694243, 9.238642140468242), (-5.355674185463666, 9.238642140468242), (-4.252917293233089, 9.238642140468242), (-3.1501604010025126, 9.238642140468242), (-2.0474035087719358, 9.238642140468242), (-0.944646616541359, 9.238642140468242), (0.15811027568921787, 9.238642140468242)}, {(-17.48600000000001, 8.134963210702352), (-16.383243107769434, 8.134963210702352), (-15.280486215538858, 8.134963210702352), (-14.17772932330828, 8.134963210702352), (-13.074972431077704, 8.134963210702352), (-11.972215538847127, 8.134963210702352), (-10.86945864661655, 8.134963210702352), (-9.766701754385974, 8.134963210702352), (-8.663944862155397, 8.134963210702352), (-7.56118796992482, 8.134963210702352), (-6.458431077694243, 8.134963210702352), (-5.355674185463666, 8.134963210702352), (-4.252917293233089, 8.134963210702352), (-3.1501604010025126, 8.134963210702352), (-2.0474035087719358, 8.134963210702352), (-0.944646616541359, 8.134963210702352), (0.15811027568921787, 8.134963210702352)}, {(-17.48600000000001, 7.031284280936464), (-16.383243107769434, 7.031284280936464), (-15.280486215538858, 7.031284280936464), (-14.17772932330828, 7.031284280936464), (-13.074972431077704, 7.031284280936464), (-11.972215538847127, 7.031284280936464), (-10.86945864661655, 7.031284280936464), (-9.766701754385974, 7.031284280936464), (-8.663944862155397, 7.031284280936464), (-7.56118796992482, 7.031284280936464), (-6.458431077694243, 7.031284280936464), (-5.355674185463666, 7.031284280936464), (-4.252917293233089, 7.031284280936464), (-3.1501604010025126, 7.031284280936464), (-2.0474035087719358, 7.031284280936464), (-0.944646616541359, 7.031284280936464), (0.15811027568921787, 7.031284280936464)}, {(-17.48600000000001, 5.927605351170575), (-16.383243107769434, 5.927605351170575), (-15.280486215538858, 5.927605351170575), (-14.17772932330828, 5.927605351170575), (-13.074972431077704, 5.927605351170575), (-11.972215538847127, 5.927605351170575), (-10.86945864661655, 5.927605351170575), (-9.766701754385974, 5.927605351170575), (-8.663944862155397, 5.927605351170575), (-7.56118796992482, 5.927605351170575), (-6.458431077694243, 5.927605351170575), (-5.355674185463666, 5.927605351170575), (-4.252917293233089, 5.927605351170575), (-3.1501604010025126, 5.927605351170575), (-2.0474035087719358, 5.927605351170575), (-0.944646616541359, 5.927605351170575), (0.15811027568921787, 5.927605351170575)}, {(-17.48600000000001, 4.8239264214046855), (-16.383243107769434, 4.8239264214046855), (-15.280486215538858, 4.8239264214046855), (-14.17772932330828, 4.8239264214046855), (-13.074972431077704, 4.8239264214046855), (-11.972215538847127, 4.8239264214046855), (-10.86945864661655, 4.8239264214046855), (-9.766701754385974, 4.8239264214046855), (-8.663944862155397, 4.8239264214046855), (-7.56118796992482, 4.8239264214046855), (-6.458431077694243, 4.8239264214046855), (-5.355674185463666, 4.8239264214046855), (-4.252917293233089, 4.8239264214046855), (-3.1501604010025126, 4.8239264214046855), (-2.0474035087719358, 4.8239264214046855), (-0.944646616541359, 4.8239264214046855), (0.15811027568921787, 4.8239264214046855)}, {(-17.48600000000001, 3.720247491638797), (-16.383243107769434, 3.720247491638797), (-15.280486215538858, 3.720247491638797), (-14.17772932330828, 3.720247491638797), (-13.074972431077704, 3.720247491638797), (-11.972215538847127, 3.720247491638797), (-10.86945864661655, 3.720247491638797), (-9.766701754385974, 3.720247491638797), (-8.663944862155397, 3.720247491638797), (-7.56118796992482, 3.720247491638797), (-6.458431077694243, 3.720247491638797), (-5.355674185463666, 3.720247491638797), (-4.252917293233089, 3.720247491638797), (-3.1501604010025126, 3.720247491638797), (-2.0474035087719358, 3.720247491638797), (-0.944646616541359, 3.720247491638797), (0.15811027568921787, 3.720247491638797)}, {(-17.48600000000001, 2.616568561872908), (-16.383243107769434, 2.616568561872908), (-15.280486215538858, 2.616568561872908), (-14.17772932330828, 2.616568561872908), (-13.074972431077704, 2.616568561872908), (-11.972215538847127, 2.616568561872908), (-10.86945864661655, 2.616568561872908), (-9.766701754385974, 2.616568561872908), (-8.663944862155397, 2.616568561872908), (-7.56118796992482, 2.616568561872908), (-6.458431077694243, 2.616568561872908), (-5.355674185463666, 2.616568561872908), (-4.252917293233089, 2.616568561872908), (-3.1501604010025126, 2.616568561872908), (-2.0474035087719358, 2.616568561872908), (-0.944646616541359, 2.616568561872908), (0.15811027568921787, 2.616568561872908)}, {(-17.48600000000001, 1.5128896321070187), (-16.383243107769434, 1.5128896321070187), (-15.280486215538858, 1.5128896321070187), (-14.17772932330828, 1.5128896321070187), (-13.074972431077704, 1.5128896321070187), (-11.972215538847127, 1.5128896321070187), (-10.86945864661655, 1.5128896321070187), (-9.766701754385974, 1.5128896321070187), (-8.663944862155397, 1.5128896321070187), (-7.56118796992482, 1.5128896321070187), (-6.458431077694243, 1.5128896321070187), (-5.355674185463666, 1.5128896321070187), (-4.252917293233089, 1.5128896321070187), (-3.1501604010025126, 1.5128896321070187), (-2.0474035087719358, 1.5128896321070187), (-0.944646616541359, 1.5128896321070187), (0.15811027568921787, 1.5128896321070187)}, {(-17.48600000000001, 0.4092107023411309), (-16.383243107769434, 0.4092107023411309), (-15.280486215538858, 0.4092107023411309), (-14.17772932330828, 0.4092107023411309), (-13.074972431077704, 0.4092107023411309), (-11.972215538847127, 0.4092107023411309), (-10.86945864661655, 0.4092107023411309), (-9.766701754385974, 0.4092107023411309), (-8.663944862155397, 0.4092107023411309), (-7.56118796992482, 0.4092107023411309), (-6.458431077694243, 0.4092107023411309), (-5.355674185463666, 0.4092107023411309), (-4.252917293233089, 0.4092107023411309), (-3.1501604010025126, 0.4092107023411309), (-2.0474035087719358, 0.4092107023411309), (-0.944646616541359, 0.4092107023411309), (0.15811027568921787, 0.4092107023411309)}, {(-17.48600000000001, -0.6944682274247587), (-16.383243107769434, -0.6944682274247587), (-15.280486215538858, -0.6944682274247587), (-14.17772932330828, -0.6944682274247587), (-13.074972431077704, -0.6944682274247587), (-11.972215538847127, -0.6944682274247587), (-10.86945864661655, -0.6944682274247587), (-9.766701754385974, -0.6944682274247587), (-8.663944862155397, -0.6944682274247587), (-7.56118796992482, -0.6944682274247587), (-6.458431077694243, -0.6944682274247587), (-5.355674185463666, -0.6944682274247587), (-4.252917293233089, -0.6944682274247587), (-3.1501604010025126, -0.6944682274247587), (-2.0474035087719358, -0.6944682274247587), (-0.944646616541359, -0.6944682274247587), (0.15811027568921787, -0.6944682274247587)}, {(-17.48600000000001, -1.7981471571906482), (-16.383243107769434, -1.7981471571906482), (-15.280486215538858, -1.7981471571906482), (-14.17772932330828, -1.7981471571906482), (-13.074972431077704, -1.7981471571906482), (-11.972215538847127, -1.7981471571906482), (-10.86945864661655, -1.7981471571906482), (-9.766701754385974, -1.7981471571906482), (-8.663944862155397, -1.7981471571906482), (-7.56118796992482, -1.7981471571906482), (-6.458431077694243, -1.7981471571906482), (-5.355674185463666, -1.7981471571906482), (-4.252917293233089, -1.7981471571906482), (-3.1501604010025126, -1.7981471571906482), (-2.0474035087719358, -1.7981471571906482), (-0.944646616541359, -1.7981471571906482), (0.15811027568921787, -1.7981471571906482)}}
  56. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, RasterMaxX / RasterStepXY, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, RasterMaxY / RasterStepXY, RasterMaxY / RasterStepXY]}) → RasterAussen

AI Drawing Prompt Reference

On one coordinate plane, draw two parallel lines and set up two angle locations formed by points and rays on those lines. Choose a reference intersection point and construct angles on the parallel lines at multiple ray directions, marking each angle with circular arc or sector shapes placed at the correct side of the intersection. Then add another slanted line that intersects the two parallel lines, creating two additional intersection points, and mark the related angles there with corresponding arc/sector regions. Use several circle sectors on both intersection points to visually highlight corresponding angles and alternate interior angles, and include space for entering angle values.
The prompt above was compiled from the original drawing commands and is for reference only.