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平行线与截线形成的角的度量

平行线与截线形成的角的度量
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2023-08-24 08:42
角解析几何变换几何作图滑块动画
本范例演示了如何通过应用角对之间的关系来确定由平行线与截线形成的角的度量。它涉及的角度关系包括同位角、内错角、同旁内角和对应角。通过使用GeoGebra命令如Sequence、Take、Segment等，可以动态地展示这些角的关系。适合初中6-8年级学生学习几何中的角度和相似性概念。

GeoGebra 命令及参数

  1. Sequence(Random[0, 99] / 100, A, 1, 200) → allRandomSeeds, {0.51, 0.38, 0.7, 0.31, 0.1, 0.13, 0.6, 0.77, 0.58, 0.9, 0.4, 0.36, 0.98, 0.81, 0.29, 0.74, 0.73, 0.34, 0.67, 0.84, 0, 0.59, 0.42, 0.08, 0.72, 0.35, 0.33, 0.02, 0.38, 0.23, 0.35, 0.75, 0.64, 0.4, 0.98, 0.15, 0.88, 0.62, 0.69, 0.74, 0.93, 0.94, 0.04, 0.13, 0.74, 0.32, 0.11, 0.63, 0.04, 0.07, 0.43, 0.23, 0.33, 0.93, 0.98, 0.77, 0.66, 0.99, 0.74, 0.57, 0.09, 0.1, 0.48, 0.87, 0.07, 0.05, 0.15, 0.98, 0.61, 0.15, 0.2, 0.44, 0.87, 0.28, 0.34, 0.6, 0.5, 0.16, 0.91, 0.47, 0.92, 0.4, 0.66, 0.07, 0.14, 0.02, 0.61, 0.9, 0.89, 0.71, 0.35, 0.11, 0.86, 0.72, 0.53, 0.32, 0.48, 0.46, 0.34, 0.93, 0.6, 0.48, 0.08, 0.76, 0.48, 0.12, 0.07, 0.47, 0.54, 0.97, 0.79, 0.9, 0.39, 0.52, 0.05, 0.49, 0.24, 0.12, 0.56, 0.35, 0.53, 0.8, 0.56, 0.44, 0.21, 0.17, 0.48, 0.94, 0.07, 0.18, 0.97, 0.19, 0.22, 0.72, 0.35, 0.63, 0.72, 0.62, 0.42, 0.1, 0.37, 0.06, 0.69, 0.48, 0.11, 0.71, 0.95, 0.85, 0.66, 0.4, 0.14, 0.2, 0.98, 0.33, 0.93, 0.96, 0.73, 0.28, 0.71, 0.86, 0.31, 0.7, 0.9, 0.82, 0.98, 0.57, 0.51, 0.24, 0.03, 0.95, 0.71, 0.58, 0.27, 0.13, 0.46, 0.5, 0.3, 0.54, 0.28, 0.83, 0.77, 0.54, 0.93, 0.45, 0.96, 0.27, 0.71, 0.78, 0.11, 0.35, 0.59, 0.58, 0.58, 0.92, 0.73, 0.4, 0.57, 0.1, 0.56, 0.75}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Segment((-3.3, 1), (3.3, 1)) → startSeg1
  4. Segment((-3.3, -1), (3.3, -1)) → startSeg2
  5. If(randOdds ≟ 1, 1 + floor((currentRandomSeeds(1) * 3)), 4) → randRelationship
  6. If(-20 + floor((currentRandomSeeds(2) * 40)) + randomAngle ≟ 90, -20 + floor((currentRandomSeeds(2) * 40)) + 1, -20 + floor((currentRandomSeeds(2) * 40))) → randomRot
  7. Rotate(startSeg1, randomRot°) → parallelSeg1
  8. Vertex(parallelSeg1, 2) → Seg1P2
  9. Vertex(parallelSeg1, 1) → Seg1P1
  10. Rotate(startSeg2, randomRot°) → parallelSeg2
  11. Vertex(parallelSeg2, 2) → Seg2P2
  12. Vertex(parallelSeg2, 1) → Seg2P1
  13. Rotate(Segment[(-3.3, 0), (3.3, 0)], randomRot°) → startSegBase
  14. Midpoint(startSegBase) → RotPoint
  15. Rotate(startSegBase, randomAngle°, RotPoint) → transversal
  16. Intersect(parallelSeg1, transversal) → Int1
  17. Intersect(parallelSeg2, transversal) → Int2
  18. Vertex(transversal, 2) → Seg1T2
  19. Vertex(transversal, 1) → Seg1T1
  20. Element(allRels, randRelationship, randomPosition) → indAngle2
  21. PixelsToDistance(8, Corner[1], Corner[3], Corner[5]) → pix8
  22. Angle(angleChoice(1), angleChoice(2), angleChoice(3)) → angle1
  23. Line(Seg1P1, Seg1P2) → parallelLine1
  24. Line(Seg2P1, Seg2P2) → parallelLine2
  25. If(randRelationship < 4, angle1, 180° - angle1) → correctAngle
  26. Polygon({(-5, -6.5), (-5, 6.5), (6, 6.5), (6, -6.5)}) → viewbox
  27. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  28. Textfield(input1) → InputBox1
  29. Corner(5) → layoutAppSize
  30. Angle(angleChoice2(1), angleChoice2(2), angleChoice2(3)) → angle2
  31. If(Mod[randomPosition, 2] ≟ 0, 1, -1) → sideAngleLR
  32. If(Mod[indAngle2, 2] ≟ 0, 1, -1) → sideXLR
  33. If(randomPosition ≤ 2 ∨ 5 ≤ randomPosition ≤ 6, 1, -1) → sideAngleTB
  34. If(indAngle2 ≤ 2 ∨ 5 ≤ indAngle2 ≤ 6, 1, -1) → sideXTB
  35. Rotate(Segment[(-3.3, 0), (3.3, 0)], randomAngle°) → transversalStart
  36. Intersect(startSeg1, transversalStart) → Int1Start
  37. Intersect(startSeg2, transversalStart) → Int2Start
  38. If(randomPosition ≤ 4, Int1Start, Int2Start) → PointAngle
  39. If(indAngle2 ≤ 4, Int1Start, Int2Start) → PointX
  40. If(sideAngleTB ≟ 1, Seg1T2, Seg1T1) → PointEndAngleY
  41. If(randomPosition ≤ 4, If[sideAngleLR ≟ 1, Seg1P2, Seg1P1], If[sideAngleLR ≟ 1, Seg2P2, Seg2P1]) → PointEndAngleX
  42. AngleLabelPosition(angleChoice(2), angleChoice(1), angleChoice(3), angleDims(1) + pix8, angleDims(2) + pix8) → PtAngle
  43. AngleLabelPosition(angleChoice2(2), angleChoice2(1), angleChoice2(3), xDims(1) + pix8, xDims(2) + pix8) → PtX
  44. If(Defined[Intersect[transversal, bottomLine]], Intersect[transversal, bottomLine], Seg1T1) → bottomInt
  45. If(Defined[Intersect[transversal, topLine]], Intersect[transversal, topLine], Seg1T2) → topInt
  46. Segment(topInt, bottomInt) → transversalDisplay
  47. If(randomPosition ≤ 4, Int1, Int2) → AnimationStart
  48. Circle(Int1, If[randomAngle ≟ 90, 0.45, 0.6]) → circleTop
  49. Circle(Int2, If[randomAngle ≟ 90, 0.45, 0.6]) → circleBottom
  50. If(randomPosition ≤ 4, circleTop, circleBottom) → circleChoice1
  51. If(randRelationship ≟ 1, circleChoice1, If[randomPosition ≤ 4, circleBottom, circleTop]) → circleChoice2
  52. CircleSector(PtsArc1(1), PtsArc1(2), PtsArc1(3)) → Arc1a
  53. CircleSector(PtsArc2(1), PtsArc2(2), PtsArc2(3)) → Arc2a
  54. CircleSector(PtsArc1(1), PtsArc1(3), PtsArc1(2)) → Arc1b
  55. CircleSector(PtsArc2(1), PtsArc2(3), PtsArc2(2)) → Arc2b
  56. If(Arc1a > (pi * 0.6^(2) / 2), Arc1b, Arc1a) → Arc1
  57. If(Arc2a > (pi * 0.6^(2) / 2), Arc2b, Arc2a) → Arc2
  58. If(randRelationship ≟ 1, AnimationStart, randomPosition ≤ 4, Int2, Int1) → EndAnimation1
  59. If(randRelationship ≟ 1, 0, randRelationship ≠ 3, animationSlider, animationSlider < 0.5, (animationSlider * 2), 1) → animationSlider1
  60. If(Mod[randRelationship, 2] ≟ 0, 0, randRelationship ≟ 1, animationSlider, animationSlider < 0.5, 0, animationSlider ≥ 0.5, ((animationSlider - 0.5) * 2), 1) → animationSlider2
  61. PartitionPoint(AnimationStart, EndAnimation1, animationSlider1, 1) → AnimationPoint1
  62. Translate(Arc1, Vector[AnimationStart, AnimationPoint1]) → animation1Arc
  63. If(randRelationship ≟ 1, Arc1, Arc2) → arcToRotate
  64. Rotate(arcToRotate, (180° * If[randRelationship ≟ 1, animationSlider, 1 - animationSlider2]), EndAnimation1) → animation2Arc
  65. Polygon({PtsArc1(1), PtsArc1(2), Mirror[PtsArc1(1), Segment[PtsArc1(2), PtsArc1(3)]], PtsArc1(3)}) → square1
  66. Polygon({PtsArc2(1), PtsArc2(2), Mirror[PtsArc2(1), Segment[PtsArc2(2), PtsArc2(3)]], PtsArc2(3)}) → square2
  67. Translate(square1, Vector[AnimationStart, AnimationPoint1]) → animation1Square
  68. If(randRelationship ≟ 1, square1, square2) → squareToRotate
  69. Rotate(squareToRotate, (180° * If[randRelationship ≟ 1, animationSlider, 1 - animationSlider2]), EndAnimation1) → animation2Square

AI 绘图提示语参考

绘制两条平行线和一条截线，展示它们相交形成的角度。平行线由两个水平线段组成，截线从上方斜向穿过平行线。交点处标记出对应角、内错角和同旁内角。图形中包含平行线段、截线、交点、角度标记和一条垂直线作为参考。构造顺序是先画平行线，再画截线，然后确定交点，最后标注角度关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。