特殊平行角

特殊平行角
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2024-04-04 21:02
所属专题 Besondere Winkelpaare
本范例演示特殊平行角的性质,包括同位角、内错角等。涉及的核心数学概念有角的分类和度量。通过构造平行线和角度,使用了GeoGebra的Segment、Angle、Translate等命令。适合5-6年级学生学习几何和角度相关知识。

GeoGebra 命令及参数

  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 绘图提示语参考

在同一坐标平面先画两条平行直线,并用点与直线构成两组角。取中间参考点,在两条平行线上分别标出四个方向的角,用扇形与圆弧在两侧相应位置表示这些角的大小;同时给出位于交点处的角度标记。再用另一条斜线与两条平行线相交,得到两处交点与对应的角扇形。通过在圆上截取多个扇形区域,把同位角、内错角及其对应角的关系以圆弧标注清晰呈现,并在下方预留可输入的角度数值区域。
以上提示语为根据原始绘图命令整理而来,仅供参考。