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命名角度：识别与标注几何角

命名角度：识别与标注几何角
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2023-06-06 00:26
角几何作图滑块动画
本范例演示如何在不同方式下命名几何角，帮助学生掌握角度的识别与标注方法。核心数学概念包括角的顶点、射线、内角与外角，以及命名规范。作图要点涉及使用GeoGebra命令如Angle、Segment、Point等来构造和标注角度。适合小学高年级学生或数学课堂练习，用于巩固几何基础技能。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 100) → randomSeeds, {0.5140206917195554, 0.3753136250769478, 0.07929392668764837, 0.32663072091856077, 0.3947710952732231, 0.8309546357688591, 0.6757631530187903, 0.22068465444417779, 0.08365238061502793, 0.29084876670942994, 0.5835386059271006, 0.2778644306908451, 0.6675260605072714, 0.1311002804604042, 0.5256634894440361, 0.8152674610116075, 0.11578221668412661, 0.406541396266655, 0.3571991594230774, 0.12373274796949953, 0.3090694690229554, 0.8015720845150307, 0.32391538159079597, 0.8829906602527673, 0.8540651522141954, 0.6783901479661024, 0.5861778202199367, 0.7874798909384869, 0.21618121868737167, 0.4039773892009437, 0.057521089705360524, 0.18893836703177103, 0.5950214306640529, 0.8787990555642525, 0.3495339692001329, 0.6114356020653277, 0.27626216507490386, 0.6352036354233397, 0.6377602459976044, 0.4025119810484186, 0.46842514056279944, 0.021976313738088223, 0.797331593908447, 0.730525929983194, 0.41374169132978245, 0.24340404605085716, 0.34200053436190453, 0.783183086554352, 0.8689787969963908, 0.6765518028425203, 0.41613015910863, 0.20553202663275077, 0.7147047476094343, 0.459229221429044, 0.1960230617399251, 0.9374592554794703, 0.000015972047418325585, 0.8133428066692434, 0.8147362322191674, 0.7509015561729458, 0.32423083325864377, 0.7639844852344866, 0.23322934567972506, 0.9056171826721069, 0.28747441230176324, 0.6336977253243141, 0.1403326941376643, 0.5494173306101401, 0.008436808466601225, 0.683892570724736, 0.4945972741460254, 0.9642580577132909, 0.9498818344372836, 0.5913476332862192, 0.9826031367631777, 0.4535279530566477, 0.6507159274200375, 0.7771411673664582, 0.09075313178581226, 0.8082397569061671, 0.7975962395461434, 0.7281950643254628, 0.4709683441106697, 0.5806453122263965, 0.09916526737143613, 0.18789548585470434, 0.7650268790543923, 0.003040501738279615, 0.9320433871465073, 0.8019698659713685, 0.8075522296685872, 0.207213096864571, 0.9296936874729049, 0.268954926317315, 0.8538579185514983, 0.8561087813239613, 0.23319329166343045, 0.9311818813869358, 0.5159941932784178, 0.2538517416767065}
  2. Shuffle(Sequence[6]) → randomCase, {3, 2, 4, 1, 6, 5}
  3. Element({{"A", "B", "C"}, {"L", "M", "N"}, {"X", "Y", "Z"}}, indexLetter) → letterSet
  4. Sequence((("\angle " * letterSet(namesFound(A, 2))) * If[Length[namesFound(A)] > 2, (letterSet(namesFound(A, 3)) * letterSet(namesFound(A, 4))), ""]), A, 1, Length[namesFound]) → foundList
  5. Element(randomCase, Mod[countQuestion, Length[randomCase]] + 1) → caseNum
  6. Element({pi / 2, pi / 3, pi / 4, (3 * pi / 5), (2 * pi / 5), (2 * pi / 3), pi / 6, (5 * pi / 6)}, indexRotation) → rotationAngle
  7. Rotate(AnchorFigure + (armLength, 0), rotationAngle, AnchorFigure) → PtB
  8. Element({pi / 2, pi / 3, pi / 4, (3 * pi / 5), (2 * pi / 5), (2 * pi / 3), pi / 6, (5 * pi / 6)}, indexAngle) → currentAngle
  9. Rotate(AnchorFigure + (armLength, 0), rotationAngle + currentAngle, AnchorFigure) → PtA
  10. Element({{PtA, AnchorFigure, AnchorFigure, PtB}, {PtB, AnchorFigure, AnchorFigure, PtA}, {AnchorFigure, PtA, AnchorFigure, PtB}}, displayCase) → displayPointsActual
  11. Element({{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}, caseNum) → caseMap
  12. If(Length[destinationOrder] ≟ 2, IndexOf[destinationOrder(2), caseMap], IndexOf[destinationOrder(3), caseMap]) → PointStudentCenter
  13. If(Length[destinationOrder] ≟ 2, Mod[PointStudentCenter, 3] + 1, IndexOf[destinationOrder(2), caseMap]) → PointStudentFirst
  14. Element(Remove[{1, 2, 3}, {PointStudentCenter, PointStudentFirst}], 1) → PointStudentThird
  15. Element({{PointStudentCenter, PointStudentFirst, PointStudentCenter, PointStudentThird}, {PointStudentFirst, PointStudentCenter, PointStudentFirst, PointStudentCenter}, {PointStudentFirst, PointStudentCenter, PointStudentCenter, PointStudentThird}}, Length[destinationOrder] - 1) → displayOrderStudent
  16. Zip(Element[{PtA, AnchorFigure, PtB}, A], A, displayOrderStudent) → displayPointsStudent
  17. If(displayCase ≟ 4, displayPointsStudent, displayPointsActual) → displayPointsAnimate
  18. Zip(Element[{PtA, AnchorFigure, PtB}, B], B, {PointStudentFirst, PointStudentCenter, PointStudentThird}) → studentPoints
  19. Element(movingPoints, movingIndex) → PMove
  20. centerBox(widths(4), boxHeight, P4) → box4
  21. centerBox(widths(3), boxHeight, P3) → box3
  22. centerBox(widths(2), boxHeight, P2) → box2
  23. centerBox(widths(1), boxHeight, P1) → box1
  24. Sequence(If[A ≟ 1, 0, boxWidth], A, 1, 4) → homeOffsets
  25. Sequence(If[A ≟ 1, boxWidth / 2, boxWidth], A, 1, Length[destinationOrder]) → destinationOffsets
  26. Append(letterSet, "\angle") → allText
  27. Sequence(HomeAnchor + (Sum[Take[homeOffsets, 1, A]] + (A * 0.2), 0), A, 1, 4) → homeLocations
  28. PointToPixels(Corner[1], Corner[3], Corner[5], homeLocations(10) + (1, -0.3)) → OnboardingStart
  29. centerBox(destinationBoxWidth, boxHeight, CenterDestination) → frameAnswer
  30. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  31. Corner(5) → layoutAppSize
  32. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  33. Element({If[layoutX ≟ 16, layoutX - 5, 11], layoutX - 5}, layoutCase) → layoutHintSolnX
  34. If(step ≟ 1 ∨ step ≟ 2 ∧ (¬showsolution), layoutY + 5, layoutY - 50) → layoutFeedbackY
  35. If(IsInRegion[PMove, frameAnswer], FRAME, HOME) → locationPMove
  36. centerBox(widths(movingIndex), boxHeight, PMove) → highlightBox
  37. Zip(HOME, A, movingPoints) → allHome
  38. Defined(IndexOf[movingIndex, destinationOrder]) → inDestination
  39. If(Defined[movingIndex], Text[allText(movingIndex), PMove, true, true, 0, 0], "") → textHighlight
  40. Sequence(DestinationAnchor + (Sum[Take[destinationOffsets, 1, A]], 0), A, 1, Length[destinationOffsets]) → destinationAnchors
  41. Zip(Text[("\vphantom{\dfrac{1}{2}}\hspace{7px}" * If[step ≟ 2 ∧ (¬Defined[IndexOf[C, destinationOrder]]), "", ("" * A)]), B, true, true, 0, 0], A, allText, B, movingPoints, C, {1, 2, 3, 4}) → boxText
  42. Sequence(letterSet(caseMap(i)), i, 1, 3) → displayOrder
  43. Angle(PtB, AnchorFigure, PtA) → angleInterior
  44. Segment(AnchorFigure, PtB) → rayB
  45. Segment(AnchorFigure, PtA) → rayA
  46. RemoveUndefined(Zip[If[IsInRegion[PMove, A] ∧ B ≠ movingIndex, B], A, {box1, box2, box3, box4}, B, {1, 2, 3, 4}]) → overlapBox
  47. If(Length[overlapBox] ≟ 1, Element[{box1, box2, box3, box4}, overlapBox(1)], centerBox[destinationBoxWidth, boxHeight, CenterDestination]) → highlightFrame
  48. Zip(centerBox[boxWidth, boxHeight, B], B, movingPoints) → allBoxes
  49. Sequence((("SetFixed(box" * A) * ",false,enableInput)"), A, 1, 4) → cmdFixBoxes
  50. RemoveUndefined(Sequence[If[¬Defined[IndexOf[A, destinationOrder]], (((("SetValue(P" * A) * ",homeLocations(") * A) * "))")], A, 1, 4]) → cmdOrganizeHome
  51. Sequence((((("SetValue(P" * A) * ",homeLocations(") * A) * "))"), A, 1, 4) → cmdSendHome
  52. Sequence((((("SetValue(P" * destinationOrder(A)) * ",destinationAnchors(") * A) * "))"), A, 1, Length[destinationOrder]) → cmdOrganizeDestination
  53. Text(("" * letterSet(correctOrder(1, 3))), Midpoint[PtA, PtB] + (1.2 * (AnchorFigure - Midpoint[PtA, PtB])), true, true, 0, 0) → lblAnchor
  54. If(displayPointsAnimate(1) ≠ displayPointsAnimate(3), If[animateControl < 1, animateControl, 1], animateControl / 2) → animate1
  55. If(displayPointsAnimate(1) ≠ displayPointsAnimate(3), If[animateControl < 1, 0, animateControl - 1], animateControl / 2) → animate2
  56. Segment(displayPointsAnimate(1), displayPointsAnimate(1) + (animate1 * (displayPointsAnimate(2) - displayPointsAnimate(1)))) → animateBranch1A
  57. Segment(displayPointsAnimate(3), displayPointsAnimate(3) + (animate2 * (displayPointsAnimate(4) - displayPointsAnimate(3)))) → animateBranch1B
  58. Length(namesFound) → numCorrect
  59. centerBox(7, 7, AnchorFigure) → coverBox
  60. If(Angle[studentPoints(1), studentPoints(2), studentPoints(3)] > pi, Angle[studentPoints(3), studentPoints(2), studentPoints(1)], Angle[studentPoints(1), studentPoints(2), studentPoints(3)]) → studentAngle
  61. Angle(PtB, AnchorFigure, PtA) → angleSoln
  62. Text(("" * letterSet(correctOrder(1, 2))), AnchorFigure + (1.2 * (PtA - AnchorFigure)), true, true, 0, 0) → lblA
  63. Text(("" * letterSet(correctOrder(1, 4))), AnchorFigure + (1.2 * (PtB - AnchorFigure)), true, true, 0, 0) → lblB
  64. Zip(displayOrder(IndexOf[A, {PtA, AnchorFigure, PtB}]), A, {displayPointsAnimate(1), displayPointsAnimate(2), displayPointsAnimate(4)}) → animatePoints
  65. Text(("" * displayOrder(1)), AnchorFigure + (1.2 * (PtA - AnchorFigure)), true, true, 0, 0) → lblAnimateFirst
  66. Text(("" * displayOrder(2)), Midpoint[PtA, PtB] + (1.2 * (AnchorFigure - Midpoint[PtA, PtB])), true, true, 0, 0) → lblAnimateSecond
  67. Text(("" * displayOrder(3)), AnchorFigure + (1.2 * (PtB - AnchorFigure)), true, true, 0, 0) → lblAnimateThird
  68. Sequence(animateControl ≥ Element[{0.1, 1, 2}, A] ∧ studentPoints(Element[{1, 2, 4}, A]) ≟ Element[{PtA, AnchorFigure, PtB}, A], A, 1, 3) → showStudent
  69. Zip(animateControl > 0 ∧ displayPointsAnimate(1) ≟ A ∨ animateControl ≥ 1 ∧ displayPointsAnimate(2) ≟ A ∧ displayPointsAnimate(1) ≠ displayPointsAnimate(3) ∨ animateControl ≟ 2 ∧ displayPointsAnimate(4) ≟ A ∧ showFinalLabel, A, {PtA, AnchorFigure, PtB}) → highlightLabels
  70. Segment(displayPointsAnimate(3), displayPointsAnimate(4)) → animateRay2
  71. Segment(displayPointsAnimate(If[displayPointsAnimate(1) ≟ displayPointsAnimate(3), 2, 1]), displayPointsAnimate(If[displayPointsAnimate(1) ≟ displayPointsAnimate(3), 1, 2])) → animateRay1
  72. Zip(expandQuad[Vertex[A, 1], Vertex[A, 2], Vertex[A, 3], Vertex[A, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]], A, Sequence[Element[{box1, box2, box3, box4}, A], A, 1, 4]) → pulsingObjects

AI 绘图提示语参考

画一个几何角度示例，包含一个顶点和两条射线，展示不同角度的命名方式。顶点位于中心，两条射线分别从顶点发出，形成不同的角度。使用不同颜色和标签清晰标识每个角度的名称，包括顶点和两条射线上的字母。先画出基本的角度结构，再添加名称标签，最后展示几种不同的角度命名方式。
以上提示语为根据原始绘图命令整理而来，仅供参考。