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Drawing Angles Using a Protractor

Drawing Angles Using a Protractor
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2022-12-21 01:30
AngleGeometric ConstructionSlider Animation
This example demonstrates how to draw angles of a given size using a protractor. The key mathematical concepts involve angle measurement and the fact that a circle measures 360 degrees. Construction involves using GeoGebra commands such as RandomUniform, Polygon, Angle, and others to create dynamic angle graphics. Suitable for elementary students or classroom practice to understand basic angle concepts and drawing techniques.

GeoGebra Commands & Parameters

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.8137602474657514, 0.3062438103764016, 0.6097102239064658, 0.06286411336398408, 0.2988247754887157, 0.3979910338126235, 0.10430735447183934, 0.22455033143884204, 0.8157351166778034, 0.8574047699951022, 0.6085637154155399, 0.9109049314721442, 0.26441995462471524, 0.5632592226993015, 0.1641216362149642, 0.4401293735704895, 0.11072879987039164, 0.928268329278164, 0.7441964283312047, 0.6789444513016941, 0.44118411757316145, 0.6812690993114908, 0.8256946371135659, 0.7856319890161692, 0.17196618147330567, 0.3303699866569479, 0.21253405057437724, 0.10600388249598819, 0.16979689348411547, 0.2861822613785002, 0.360560746387816, 0.7355138985765768, 0.7127687323656955, 0.559243301815275, 0.3434330234841677, 0.018060937197297688, 0.3242340127570959, 0.6229176360143929, 0.19750416697003143, 0.5365543503327381, 0.952625047711478, 0.002427951648928313, 0.9820853840188972, 0.37202093122125685, 0.7845196790988612, 0.5422196502190998, 0.8195079122393081, 0.1369292899848916, 0.7573966104676414, 0.21760405229983737, 0.7171271165299068, 0.3044918310663479, 0.7323446309618534, 0.24255213863309294, 0.6508242912498573, 0.2589754818586227, 0.43549439173176424, 0.31362642500601123, 0.04666093599162182, 0.7825118885411194, 0.18013554963008388, 0.410341240318355, 0.6141277029154869, 0.9015437373840272, 0.19936275840777976, 0.27473183810173224, 0.880904502020125, 0.8108782134368809, 0.4016621240018666, 0.39759052527427907, 0.4552108583436939, 0.725339898362658, 0.5491060706979806, 0.655693131567394, 0.9776747421532369, 0.17822462360950372, 0.18976736295150717, 0.31339225893189515, 0.9001852739100294, 0.032151827717003444, 0.1325943145070234, 0.18319330809602055, 0.9644197189127663, 0.1914975433343327, 0.9543074284389776, 0.27335780192458387, 0.21764685184713856, 0.39636109191762775, 0.753883483189296, 0.9661931208960345, 0.2680083871985672, 0.03597795737447448, 0.2608866171300605, 0.19849080996821036, 0.735767781871102, 0.19463749189374815, 0.7392867218020394, 0.5755658396593714, 0.10098959539823986, 0.505498228506839, 0.18847368255916733, 0.8325266958415479, 0.5217753962176087, 0.377215119246303, 0.6879322064582051, 0.0007720831959965035, 0.22053121521557287, 0.3650018670830243, 0.701485118221244, 0.9542615241029143, 0.12877914522591474, 0.4216481314496633, 0.3411436170438701, 0.30884886485664, 0.18375008237875945, 0.5550950972497956, 0.9494219255483315, 0.858894206218004, 0.11240643648424072, 0.2974450187500107, 0.20247919802241368, 0.6784856581079791, 0.23064400941129534, 0.015738315782320638, 0.9646449339515825, 0.649905011837268, 0.9072084087855885, 0.7574794605575633, 0.007765258214203629, 0.8294612226979688, 0.14333664851556782, 0.8137259119751014, 0.436375469799075, 0.9404940794959553, 0.07029656830950089, 0.45957633013450344, 0.2519603034280163, 0.2252147142548106, 0.6178460453157782, 0.9061032305187183, 0.39650680293788537, 0.941103362911431, 0.9571712328854733, 0.5491714985813986, 0.3571852914052726, 0.5338242055430454, 0.05208809669862052, 0.6391686073538666, 0.040312422647207004, 0.04704524621032214, 0.6122025421038207, 0.8514433847097609, 0.1837564021073334, 0.2601664151350334, 0.691325569096488, 0.8202093268154741, 0.9526371543408872, 0.3777615666791719, 0.14372525204447423, 0.7788153074876507, 0.9435559972088063, 0.4095307348409308, 0.6997737650583599, 0.1466197177252994, 0.5676568959914017, 0.046736167730034285, 0.9112080502612911, 0.4872265212612964, 0.8325777413908454, 0.6904613442793492, 0.4545738116243559, 0.02454987531813154, 0.49779324375625444, 0.8485847723072109, 0.5894584548947781, 0.04207079128561589, 0.746981964981508, 0.6621004818035886, 0.1258442526649966, 0.3067335438312079, 0.17486843910331007, 0.8373451445289917, 0.4523240409268853, 0.5422005151598844, 0.05449692336593456, 0.6788066085331007, 0.5040223391374213, 0.416643417983654, 0.9440870618136158, 0.9274916027053689, 0.8158512566047948, 0.5078954025990042, 0.2605022466195847, 0.7023208076198433, 0.4732054265048332, 0.7736224055516332, 0.458930100312238, 0.4466965933629691, 0.4383623738933385, 0.8861935347347519}
  2. Polygon({(-4.5, -3.7), (4.5, -3.7), (4.5, 3.7), (-4.5, 3.7)}) → graphicArea
  3. Sequence(((2 * cos(ii)), (2 * sin(ii))), ii, 0°, 360°, 1°) → PointsRayMovable
  4. Point(PointsRayMovable) → EndPointRay2
  5. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  6. Sequence(((2 * cos(ii)), (2 * sin(ii))), ii, 5°, 360°, 2°) → PointsRayFixed
  7. Element(PointsRayFixed, randomNum2) → EndPointRay1
  8. IntersectPath(Ray[Center, EndPointRay1], graphicArea) → Ray1
  9. If(Defined[Slope[Ray1]], y ≥ (Slope[Ray1] * x), x ≥ 0) → reg1
  10. Min(Angle[Vector[EndPointRay1], Vector[(1, 0)]], Angle[Vector[(1, 0)], Vector[EndPointRay1]]) → rotAngleRightProt
  11. Sequence(10, 175, 1) → angles
  12. Element(angles, randomNum1) → randomAngle
  13. Dilate(EndPointRay1, r / 2) → IniCorrectArc
  14. Rotate(IniCorrectArc, (randomAngle° * If[RotateRight, 1, -1])) → EndCorrectArc
  15. Circle(ProtractorCenter_{1}, r) → ProtractorCircle_{1}
  16. Point(ProtractorCircle_{1}) → ProtractorLeft_{1}
  17. DynamicCoordinates(ProtractorLeft_{1}, x(ProtractorLeft_{1}), y(ProtractorLeft_{1})) → ProtractorLeftDyn_{1}
  18. Point(ProtractorCircle_{1}) → ProtractorRight_{1}
  19. DynamicCoordinates(ProtractorRight_{1}, x(ProtractorRight_{1}), y(ProtractorRight_{1})) → ProtractorRightDyn_{1}
  20. Arc(ProtractorCircle_{1}, ProtractorRightDyn_{1}, ProtractorLeftDyn_{1}) → c
  21. Intersect(c, LineBisector[ProtractorRightDyn_{1}, ProtractorLeftDyn_{1}]) → D, E
  22. If(x(D) ≥ 0 ∧ y(D) ≥ 0, If[standardSol, 1, 3], x(D) < 0 ∧ y(D) ≥ 0, If[standardSol, 2, 4], x(D) < 0 ∧ y(D) < 0, If[standardSol, 3, 1], If[standardSol, 4, 2]) → quadrantProtractorCenter
  23. Dilate(Dilate[EndPointRay1, r / 2], 1.02) → IniIncorrectArc
  24. Angle(Vector[EndPointRay1], Vector[EndPointRay2]) → angleToShow
  25. Textfield(input1) → InputBox1
  26. Corner(5) → layoutAppSize
  27. sectorPixels(A, B, C, haloPixels + 40, Corner[1], Corner[3], Corner[5]) → pulsingObject
  28. sectorPixels(A, B, C, 40, Corner[1], Corner[3], Corner[5]) → displayAngle
  29. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  30. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  31. IntersectPath(Ray[Center, EndPointRay2], graphicArea) → Ray2
  32. Translate((0, 0), v) → LabelPosAngleToShow
  33. If(quadrantProtractorCenter ≟ 4, If[altSol, 4, 2], quadrantProtractorCenter ≟ 2, If[altSol, 2, 4], quadrantProtractorCenter ≟ 3, If[altSol, 3, 1], If[altSol, 1, 3]) → quadrantLegend
  34. Element(LegendPositions, quadrantLegend) → Legend2
  35. Translate(Legend1, (0, -0.5)) → Legend3
  36. Translate(Legend2, (0, -0.5)) → Legend4
  37. Segment(Legend2, Legend1) → segmentLegendCorrect
  38. Segment(Legend4, Legend3) → segmentLegendIncorrect
  39. Text("\textsf{ Correct solution\\}", Legend1, true, true, If[2 ≤ quadrantLegend ≤ 3, -1, 1], 0) → legendCorrect
  40. Text("\textsf{ Your solution\\}", Legend3, true, true, If[2 ≤ quadrantLegend ≤ 3, -1, 1], 0) → legendIncorrect
  41. Sector(x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), IniCorrectArc, EndCorrectArc) → CorrectArc1
  42. Sector(x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), EndCorrectArc, IniCorrectArc) → CorrectArc2
  43. Dilate(Dilate[EndPointRay2, r / 2], 1.02) → EndIncorrectArc
  44. Arc(x^(2) + y^(2) = Distance[Center, IniIncorrectArc]^(2), IniIncorrectArc, EndIncorrectArc) → IncorrectArc1
  45. Arc(x^(2) + y^(2) = Distance[Center, IniIncorrectArc]^(2), EndIncorrectArc, IniIncorrectArc) → IncorrectArc2
  46. Segment(Center, EndIncorrectArc) → segmentCorrect
  47. Text((input1 * "°"), (x(Dilate[EndIncorrectArc, 1.1]), Max[y(Dilate[EndIncorrectArc, 1.1]), -3.55]), true, true, 0, 0) → labelPointIncorrect
  48. Rotate(IniCorrectArc, ((anim * randomAngle°) * If[RotateRight, 1, -1])) → IniCorrectArc'
  49. Arc(x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), IniCorrectArc, IniCorrectArc') → arcAnim1
  50. Arc(x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), IniCorrectArc', IniCorrectArc) → arcAnim2
  51. circlePixels(ProtractorLeftDyn_{1}, 5 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObjectLeft
  52. circlePixels(ProtractorRightDyn_{1}, 5 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObjectRight
  53. circlePixels(ProtractorCenter_{1}, 5 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObjectCenter
  54. Text("\alpha", LabelPosAngleToShow, true, true, 0, 0) → labelAngleToShow
  55. Mirror(IniIncorrectArc, Line[(0, 0), EndPointRay1]) → IniIncorrectArc'
  56. Mirror(EndIncorrectArc, Line[(0, 0), EndPointRay1]) → EndIncorrectArc'
  57. Mirror(EndIncorrectArc, Line[(0, 0), EndPointRay1]) → EndIncorrectArc'_{1}
  58. Mirror(IniIncorrectArc, Line[(0, 0), EndPointRay1]) → IniIncorrectArc'_{1}
  59. Mirror(IniCorrectArc, Line[(0, 0), EndPointRay1]) → IniCorrectArc'_{1}
  60. Mirror(EndCorrectArc, Line[(0, 0), EndPointRay1]) → EndCorrectArc'
  61. Mirror(EndCorrectArc, Line[(0, 0), EndPointRay1]) → EndCorrectArc'_{1}
  62. Mirror(IniCorrectArc, Line[(0, 0), EndPointRay1]) → IniCorrectArc'_{2}
  63. Min(Angle[Vector[EndPointRay1], Vector[(-1, 0)]], Angle[Vector[(-1, 0)], Vector[EndPointRay1]]) → rotAngleLeftProt
  64. Rotate(pic1, 180°) → pic1'
  65. Segment(Center, IniCorrectArc') → segAnim
  66. Sector(Mirror[x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), Line[(0, 0), EndPointRay1]], IniCorrectArc'_{1}, EndCorrectArc') → CorrectArc1'
  67. Sector(Mirror[x^(2) + y^(2) = Distance[Center, IniCorrectArc]^(2), Line[(0, 0), EndPointRay1]], EndCorrectArc'_{1}, IniCorrectArc'_{2}) → CorrectArc2'
  68. circlePixels(EndPointRay2, 9 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObjectAngle

AI Drawing Prompt Reference

Draw a coordinate-plane graphic showing a protractor-style angle construction. Use a fixed center point and a circle of radius r, then create two rays from the center whose endpoints lie on the circle. Build a protractor arc on the circle between the two ray endpoints, and use the bisector of the two rays to decide which quadrant the arc center belongs to, placing the protractor marking accordingly. Compute and display the angle formed by the two rays at the center, with a text input allowing the angle value to vary. Also show two arcs for comparison: a “correct” arc obtained by rotating the initial arc by the chosen angle, and a “your solution” arc coming from the second ray; connect relevant points to the center with short segments and add two labeled texts indicating Correct solution and Your solution.
The prompt above was compiled from the original drawing commands and is for reference only.