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Supplementary Angles by Parallel Lines and Transversal

Supplementary Angles by Parallel Lines and Transversal
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2023-09-02 01:35
AngleGeometric Construction
This example demonstrates the supplementary angle pairs formed when a transversal intersects parallel lines. Key math concepts include supplementary angle relationships, properties of parallel lines, and the role of a transversal. GeoGebra commands like Segment, Point, Line, and Angle are used to construct the parallel lines and transversal, and to measure and display the supplementary angle pairs. Suitable for students in grades 6-8 to explore angle relationships involving parallel lines and transversals, identifying congruent and supplementary angles.

GeoGebra Commands & Parameters

  1. RandomUniform(0, 0.99, 200) → allRandoms, {0.6852542497325684, 0.5267162044095176, 0.9458499873347409, 0.9409333298243145, 0.034461331510179806, 0.21689309059118983, 0.3212119310839995, 0.25100331049731084, 0.9616787843877543, 0.9671057129364996, 0.30423625188103304, 0.012906807081394854, 0.09168766843407064, 0.05152270362787516, 0.5323730437143861, 0.6691461547324542, 0.011622441221226763, 0.2120458779025743, 0.05426896435822317, 0.12000726132566775, 0.4490638602572709, 0.5768386117357381, 0.892842145073393, 0.8488365001728163, 0.11073024852233264, 0.9129851982709758, 0.12859688837538186, 0.6262360377401947, 0.2783229436220725, 0.05526527983984395, 0.36877219692912744, 0.22165961874174422, 0.03701763812549824, 0.036258572481420163, 0.9323228093043474, 0.7983424392699878, 0.7794663318326355, 0.24216599039101622, 0.9485727861919663, 0.9558875873696723, 0.33398512482492876, 0.6238398523475264, 0.36866143123101025, 0.11415707382617964, 0.23985106843543674, 0.9035616661599736, 0.8536177620809081, 0.8023796464643602, 0.08531695151481324, 0.6550874410110393, 0.4910542269942778, 0.19858863817980063, 0.5150759070154551, 0.8274013625611555, 0.7340621670446367, 0.656641735604721, 0.33346821173937335, 0.5314752200129728, 0.86092077235926, 0.4711505947188757, 0.5877207528646767, 0.444126591017097, 0.05269804596037948, 0.2346622619380253, 0.811945201059533, 0.6638007696825294, 0.4877265711280374, 0.626385159820308, 0.6274940501239942, 0.4297715648015048, 0.7072789578560704, 0.057641263713352146, 0.6685837670831658, 0.488863322801488, 0.7755466145676341, 0.5460520705325077, 0.6238432327649913, 0.8123417722823629, 0.5392427673028242, 0.46823020883294275, 0.24463018090737704, 0.5901033493602389, 0.16780474834323073, 0.3694487148237828, 0.6795822993113776, 0.3997128288578, 0.2142623700735126, 0.5283996572390021, 0.23192936620445062, 0.9341963230042809, 0.1393684075074554, 0.7257294535201131, 0.4015917550598339, 0.5547919608735212, 0.6775543211464149, 0.8865518131114338, 0.7180251340931901, 0.36309244159409043, 0.8526782542803295, 0.4095908888370462, 0.022145328375549743, 0.7611842129599584, 0.3143745254527193, 0.09899532108732491, 0.8964770018646667, 0.7484948746053982, 0.6820926405983688, 0.9091904576887739, 0.1919181663687549, 0.40010566569327094, 0.20363129137021474, 0.8683994873752379, 0.46719847236241996, 0.6532684204339088, 0.19812646704779266, 0.7126654513546424, 0.6032312779551882, 0.6167857033858223, 0.36004500325092204, 0.3393448890431621, 0.03912132995790136, 0.2217710504425234, 0.560764101997723, 0.1871196847885849, 0.8195868189656859, 0.40210064103849397, 0.7977841302750948, 0.21858792853299536, 0.07499066027148604, 0.6586002006868785, 0.3785261169501963, 0.4514451163057487, 0.005049038940356363, 0.07268097891877812, 0.7060076319114925, 0.46515623029573533, 0.14559526022096456, 0.7127462365247367, 0.2874694797946453, 0.7018452942562909, 0.4145254473921487, 0.8302340553435503, 0.16424292407074564, 0.9328921046768872, 0.5082382266846623, 0.7516452682162587, 0.001800939855449968, 0.6764282190875313, 0.943502952790608, 0.218324948840374, 0.16302944410349024, 0.9455613963825277, 0.35175241248932426, 0.507123351788728, 0.5552831357790915, 0.34273546052406195, 0.9432935541788521, 0.37235720111221615, 0.902757487679254, 0.892144787757963, 0.16786510282149666, 0.5827244376746283, 0.9401134478164265, 0.029574948617283606, 0.10534455258072796, 0.665995865303914, 0.5711317582357137, 0.2774288373290482, 0.11621716873030698, 0.23941406451627015, 0.3774549116404469, 0.5120245070522843, 0.26566760394856814, 0.06477509271377636, 0.017189633957669, 0.7705138312141763, 0.35784089592279955, 0.06415124178268956, 0.8712990308531715, 0.8259733040530657, 0.3779415881845779, 0.09513219449090084, 0.17730354134283066, 0.27135569097663376, 0.6694015021092606, 0.553320452207343, 0.9848403732797946, 0.7460686359495442, 0.9013437561316947, 0.5746106643763592, 0.14609746244199273, 0.892959185175052, 0.8580066959972631, 0.7605160775468996, 0.736042146485229, 0.2584347540546221, 0.4366641511951772, 0.2964741506613543, 0.07270686894171391, 0.5443395037797777}
  2. Segment(intersectP1(1) + (0.9, 0), intersectP1(2) - (0.9, 0)) → segP1Range
  3. Point(segP1Range) → InputPoint1
  4. Segment(intersectP2(1) + (0.9, 0), intersectP2(2) - (0.9, 0)) → segP2Range
  5. Point(segP2Range) → InputPoint2
  6. Take(allRandoms, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  7. Polygon({(-2.5, -2.5), (-2.5, 2.2), (2.5, 2.2), (2.5, -2.5)}) → graphArea
  8. Flatten(Sequence[{-1, 0, 1}, n, 1, 33]) → randomList1
  9. Element(randomList1, Mod[countQuestion, 100] + 1) → randomNum1
  10. If(y3b < -1.8 - 44 / 90, (x1 * y3b) + 0.1 + 44 / 90, x(InputPoint2) + 0.8 + 44 / 90) → x3min
  11. If(x3min < 2.5 - 44 / 90, x3min + (currentRandomSeeds(12) * (2.5 - 44 / 90 - x3min)), 3) → x3b
  12. If(y3a < -1.8 - 44 / 90, (x1 * y3a) - 0.1 - 44 / 90, x(InputPoint2) - 1.8 - 44 / 90) → x3max
  13. If(x3max > -2.5 + 44 / 90, -2.5 + 44 / 90 + (currentRandomSeeds(11) * (x3max + 2.5 - 44 / 90)), -3) → x3a
  14. If(y1b > 1.8 + 44 / 90, (x1 * y1b) + 0.1 + 44 / 90, x(InputPoint1) + 0.8 + 44 / 90) → x1min
  15. If(x1min < 2.5 - 44 / 90, x1min + (currentRandomSeeds(8) * (2.5 - 44 / 90 - x1min)), 3) → x1b
  16. If(y1a > 1.8 + 44 / 90, (x1 * y1a) - 0.1 - 44 / 90, x(InputPoint1) - 0.8 - 44 / 90) → x1max
  17. If(x1max > -2.5 + 44 / 90, -2.5 + 44 / 90 + (currentRandomSeeds(7) * (x1max + 2.5 - 44 / 90)), -3) → x1a
  18. If(x1 ≟ 1, 1 - 0.8 - 44 / 90, 0.9 - 44 / 90) → y2bmax
  19. If(x1 ≟ -1, -1 + 0.8 + 44 / 90, -0.9 + 44 / 90) → y2bmin
  20. If(y2b > -0.2 + 44 / 90 ∨ x1 ≟ 1, (x1 * y2b) + 0.1 + 44 / 90, x1 ≟ 0, 0.8 + 44 / 90, 1.8 + 44 / 90) → x2min
  21. If(x2min < 2.5 - 44 / 90, x2min + (currentRandomSeeds(10) * (2.5 - 44 / 90 - x2min)), 3) → x2b
  22. If(x1 ≟ -1, 1 - 0.8 - 44 / 90, 0.9 - 44 / 90) → y2amax
  23. If(x1 ≟ 1, -1 + 0.8 + 44 / 90, -0.9 + 44 / 90) → y2amin
  24. If(y2a < 0.2 - 44 / 90 ∨ x1 ≟ 1, (x1 * y2a) - 0.1 - 44 / 90, x1 ≟ 0, -0.8 - 44 / 90, -1.8 - 44 / 90) → x2max
  25. If(x2max > -2.5 + 44 / 90, -2.5 + 44 / 90 + (currentRandomSeeds(9) * (x2max - 44 / 90 + 2.5)), -3) → x2a
  26. KeepIf(IsInRegion[n, graphArea], n, {(x1a, y1a), (x2a, y2a), (x2b, y2b), (x3a, y3a), (x1b, y1b), (x3b, y3b)}) → treePoints
  27. If(x1 ≟ -1, 2, x1 ≟ 1, 3, 4) → case
  28. Line(InputPoint1, InputPoint2) → lineT
  29. Circle(InputPoint1, 0.8) → arcCircle1
  30. Element({{(-1.56569, 1.56569), (-0.43431, 0.43431)}, {(1.56569, 1.56569), (0.43431, 0.43431)}, {(0, 1.8), (0, 0.2)}}, case - 1) → ints2
  31. Element({{(-1.8, 1), (-0.2, 1)}, {(0.2, 1), (1.8, 1)}, {(-0.8, 1), (0.8, 1)}}, case - 1) → ints1
  32. CircleSector(InputPoint1, ints1(1), ints2(2)) → arc1
  33. CircleSector(InputPoint1, ints2(2), ints1(2)) → arc2
  34. Circle(InputPoint1, 0.7) → polyCircle1
  35. Segment(intersectP1(1), intersectP1(2)) → segmentP1
  36. Segment(intersectP1(1) - (0, 0.1), intersectP1(2) - (0, 0.1)) → lineTopB
  37. Segment(intersectP1(1) + (0, 0.1), intersectP1(2) + (0, 0.1)) → lineTopT
  38. Circle(InputPoint2, 0.7) → polyCircle2
  39. If(clickNum ≤ 4, polyCircle1, polyCircle2) → chosenCircle
  40. Segment(InputPoint1, InputPoint2) → segmentT
  41. Angle(segmentT, segmentP1) → tpAngle
  42. Element({{(-2.2, 2.2), (2.5, -2.5)}, {(2.2, 2.2), (-2.5, -2.5)}, {(0, 2.2), (0, -2.5)}}, case - 1) → intersectT
  43. If(y(Element[intersectT, 1]) < 2.2, (0, distT2), (distT, 0)) → PointDistTop
  44. If(y(Element[intersectT, 2]) > -2.5, (0, distT2), (distT, 0)) → PointDistBottom
  45. Segment(intersectT(1) + PointDistTop, intersectT(2) + PointDistBottom) → lineTransB
  46. Segment(intersectT(1) - PointDistTop, intersectT(2) - PointDistBottom) → lineTransT
  47. Circle(InputPoint2, 0.8) → arcCircle2
  48. Element({{(0.43431, -0.43431), (1.56569, -1.56569)}, {(-0.43431, -0.43431), (-1.56569, -1.56569)}, {(0, -0.2), (0, -1.8)}}, case - 1) → ints4
  49. Element({{(0.2, -1), (1.8, -1)}, {(-1.8, -1), (-0.2, -1)}, {(-0.8, -1), (0.8, -1)}}, case - 1) → ints3
  50. Vector(centerP1, arc2Ints(clickNum)) → dist1PS'
  51. Segment(intersectP2(1) - (0, 0.1), intersectP2(2) - (0, 0.1)) → lineBottomB
  52. Segment(intersectP2(1) + (0, 0.1), intersectP2(2) + (0, 0.1)) → lineBottomT
  53. Element({{(-1.04142, 0.9), (-0.75858, 0.9), (-0.95858, 1.1), (-1.24142, 1.1), (0.95858, -1.1), (1.24142, -1.1), (1.04142, -0.9), (0.75858, -0.9)}, {(0.75858, 0.9), (1.04142, 0.9), (1.24142, 1.1), (0.95858, 1.1), (-1.24142, -1.1), (-0.95858, -1.1), (-0.75858, -0.9), (-1.04142, -0.9)}, {(-0.1, 0.9), (0.1, 0.9), (0.1, 1.1), (-0.1, 1.1), (-0.1, -1.1), (0.1, -1.1), (0.1, -0.9), (-0.1, -0.9)}}, case - 1) → innerCenterInts
  54. Element({{(-1.05325, 0.87143), (-0.6896, 0.87143), (-0.94675, 1.12857), (-1.3104, 1.12857), (0.94675, -1.12857), (1.3104, -1.12857), (1.05325, -0.87143), (0.6896, -0.87143)}, {(0.6896, 0.87143), (1.05325, 0.87143), (1.3104, 1.12857), (0.94675, 1.12857), (-1.3104, -1.12857), (-0.94675, -1.12857), (-0.6896, -0.87143), (-1.05325, -0.87143)}, {(-0.12857, 0.87143), (0.12857, 0.87143), (0.12857, 1.12857), (-0.12857, 1.12857), (-0.12857, -1.12857), (0.12857, -1.12857), (0.12857, -0.87143), (-0.12857, -0.87143)}}, case - 1) → dilatedCenters
  55. Vector(centerP1, arc1Ints(clickNum)) → dist1PS
  56. Intersect(chosenCircle, Ray[dilatedCenters(clickNum), dist1PS]) → PP1,
  57. Intersect(chosenCircle, Ray[dilatedCenters(clickNum), dist1PS']) → PP2,
  58. Vector(centerP1, dilatedCenters(clickNum)) → distCPI
  59. Element({{(-1.7, 1), (-0.3, 1)}, {(0.3, 1), (1.7, 1)}, {(-0.7, 1), (0.7, 1)}}, case - 1) → ints1p
  60. Polygon({intersectP1(1) + (0, 0.1), intersectP1(1) - (0, 0.1), intersectP1(2) - (0, 0.1), intersectP1(2) + (0, 0.1)}) → streetP1
  61. Polygon({intersectT(1) + PointDistTop, intersectT(1) - PointDistTop, intersectT(2) - PointDistBottom, intersectT(2) + PointDistBottom}) → streetTransversal
  62. Element({{(-1.49497, 1.49497), (-0.50503, 0.50503)}, {(1.49497, 1.49497), (0.50503, 0.50503)}, {(0, 1.7), (0, 0.3)}}, case - 1) → ints2p
  63. Element({{(0.50503, -0.50503), (1.49497, -1.49497)}, {(-0.50503, -0.50503), (-1.49497, -1.49497)}, {(0, -0.3), (0, -1.7)}}, case - 1) → ints4p
  64. Element({{(0.3, -1), (1.7, -1)}, {(-1.7, -1), (-0.3, -1)}, {(-0.7, -1), (0.7, -1)}}, case - 1) → ints3p
  65. Angle(PolyA, centerP1, PolyB) → α
  66. Polygon({intersectP2(1) + (0, 0.1), intersectP2(1) - (0, 0.1), intersectP2(2) - (0, 0.1), intersectP2(2) + (0, 0.1)}) → streetP2
  67. If(clickNum ≟ 3 ∨ clickNum ≟ 4 ∨ clickNum ≟ 7 ∨ clickNum ≟ 8, 1, -1) → signDirectionY
  68. If(clickNum ≟ 1 ∨ clickNum ≟ 4 ∨ clickNum ≟ 5 ∨ clickNum ≟ 8, -1, 1) → signDirectionX
  69. Point(segmentT) → DragPoint
  70. Element({{(-1.79373, 0.9), (-0.36804, 0.50946), (-0.20627, 1.1), (-1.63196, 1.49054), (0.20627, -1.1), (1.63196, -1.49054), (1.79373, -0.9), (0.36804, -0.50946)}, {(0.20627, 0.9), (0.50946, 0.36804), (1.79373, 1.1), (1.49054, 1.63196), (-1.79373, -1.1), (-1.49054, -1.63196), (-0.20627, -0.9), (-0.50946, -0.36804)}, {(-0.79373, 0.9), (0.1, 0.20627), (0.79373, 1.1), (-0.1, 1.79373), (-0.79373, -1.1), (0.1, -1.79373), (0.79373, -0.9), (-0.1, -0.20627)}}, case - 1) → innerArc1
  71. Element({{(-0.50946, 0.36804), (-0.20627, 0.9), (-1.49054, 1.63196), (-1.79373, 1.1), (1.49054, -1.63196), (1.79373, -1.1), (0.50946, -0.36804), (0.20627, -0.9)}, {(0.36804, 0.50946), (1.79373, 0.9), (1.63196, 1.49054), (0.20627, 1.1), (-1.63196, -1.49054), (-0.20627, -1.1), (-0.36804, -0.50946), (-1.79373, -0.9)}, {(-0.1, 0.20627), (0.79373, 0.9), (0.1, 1.79373), (-0.79373, 1.1), (-0.1, -1.79373), (0.79373, -1.1), (0.1, -0.20627), (-0.79373, -0.9)}}, case - 1) → innerArc2
  72. Vector(centerP1, innerCenterInts(clickNum)) → distCP
  73. Rotate(dist1P, (-2 * α / 3)) → dist3P
  74. Rotate(dist1P, ((-α)) / 3) → dist2P
  75. Polygon({InputPoint1, ints1(1), (x(ints1(1)), y(ints2(2))), ints2(2)}) → square1
  76. Polygon({InputPoint1, ints2(2), (x(ints1(2)), y(ints2(2))), ints1(2)}) → square2
  77. Polygon({InputPoint1, ints1(2), (x(ints1(2)), y(ints2(1))), ints2(1)}) → square3
  78. Polygon({InputPoint1, ints2(1), (x(ints1(1)), y(ints2(1))), ints1(1)}) → square4
  79. Polygon({InputPoint2, ints3(1), (x(ints3(1)), y(ints4(2))), ints4(2)}) → square1a
  80. Polygon({InputPoint2, ints4(2), (x(ints3(2)), y(ints4(2))), ints3(2)}) → square2a
  81. Polygon({InputPoint2, ints3(2), (x(ints3(2)), y(ints4(1))), ints4(1)}) → square3a
  82. Polygon({InputPoint2, ints4(1), (x(ints3(1)), y(ints4(1))), ints3(1)}) → square4a
  83. Zip({m, n, p}, n, arc1IntsP, m, arcInputs, p, arc2IntsP) → polyPointsP
  84. Element({square1, square2, square3, square4, square1a, square2a, square3a, square4a}, transClick) → squareChoice
  85. If(clickNum ≤ 4, polyCircle2, polyCircle1) → circleDrag
  86. Point(circleDrag) → DragPointNew
  87. Angle(DragPointNew, centerP2, DragStartNew) → angleMoved
  88. If(clickNum ≟ 1 ∨ clickNum ≟ 4 ∨ clickNum ≟ 5 ∨ clickNum ≟ 8, 3, 4) → caseEnd
  89. If(case ≟ 1, 3, case ≟ 2, 7, case ≟ 3, 2, 6) → caseChoice
  90. If(centerP1 ≟ InputPoint1, InputPoint2, InputPoint1) → endPoint
  91. Rotate(DragStartNew, 180°, centerP2) → EndPoint
  92. Vector(centerP2, DragPointNew) → dist1PN
  93. Rotate(dist1PN, α / 3) → dist6PN
  94. Rotate(dist1PN, α) → dist4PN
  95. Rotate(dist1PN, (2 * α / 3)) → dist2PN
  96. Segment(intersectP2(1), intersectP2(2)) → segmentP2
  97. If(clickNum ≟ 9 ∧ case ≟ 1 ∨ showArc2 ∧ (transClick ≟ 3 ∨ transClick ≟ 4) ∨ (¬showArc2) ∧ (clickNum ≟ 3 ∨ clickNum ≟ 4), -1 - 0.5, clickNum ≟ 9 ∧ case ≟ 2 ∨ showArc2 ∧ (transClick ≟ 7 ∨ transClick ≟ 8) ∨ (¬showArc2) ∧ (clickNum ≟ 7 ∨ clickNum ≟ 8), 1 - 0.5, clickNum ≟ 9 ∧ case ≟ 3 ∨ showArc2 ∧ (transClick ≟ 1 ∨ transClick ≟ 2) ∨ (¬showArc2) ∧ (clickNum ≟ 1 ∨ clickNum ≟ 2), -1 + 0.5, 1 + 0.5) → yPixelPoint1
  98. 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
  99. Corner(5) → layoutAppSize
  100. CircleSector(InputPoint1, ints1(2), ints2(1)) → arc3
  101. CircleSector(InputPoint1, ints2(1), ints1(1)) → arc4
  102. CircleSector(InputPoint2, ints3(1), ints4(2)) → arc1a
  103. CircleSector(InputPoint2, ints4(2), ints3(2)) → arc2a
  104. CircleSector(InputPoint2, ints3(2), ints4(1)) → arc3a
  105. CircleSector(InputPoint2, ints4(1), ints3(1)) → arc4a
  106. Sequence(clickNum ≟ n, n, 1, 9) → active
  107. Zip({m, n, p}, n, arc1Ints, m, arcInputs, p, arc2Ints) → polyPoints
  108. Rotate(squareChoice, (-angleMoved), centerP2) → staticDragSquare
  109. If(Mod[clickNum, 4] > 1, 0.25, -0.25) → direction
  110. PointToPixels(Corner[1], Corner[3], Corner[5], PixelPoint) → RightPixelCoords
  111. Polygon(DragPointNew - dist1PN, DragPointNew, DragPointNew - dist7PN, DragPointNew - dist3PN, DragPointNew - dist5PN) → dragPoly2, dragPoly2a, dragPoly2b, dragPoly2c, dragPoly2d, dragPoly2e
  112. Zip(Vector[PointTreeMiddle, n], n, treePoints) → vectorTreePics
  113. Zip(Translate[treePicBase, Vector[n]], Vector[n], vectorTreePics) → trees
  114. sectorPixels(sectorUse(1), sectorUse(2), sectorUse(3), basePixels + haloPixels, Corner[1], Corner[3], Corner[5]) → pulsingObject1
  115. Dilate(DragPointNew, 8 / 7, centerP2) → DragPointNew'
  116. Polygon(DragPoint, DragPoint + distCPI, DragPoint - dist1P + distCPI, DragPoint - dist2P + distCPI, DragPoint - dist3P + distCPI, DragPoint - dist4P + distCPI, DragPoint + distCPI) → dragPoly1, dragPoly1b, dragPoly1c, dragPoly1d, dragPoly1e, dragPoly1f, dragPoly1g, dragPoly1a
  117. CircleSector(centerP2, DragPointNew', Rotate[DragPointNew', α, centerP2]) → staticDragArc2
  118. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  119. CircleSector(arcCover1(1), arcCover1(3), arcCover1(2)) → arcCoverA
  120. CircleSector(arcCover2(1), arcCover2(3), arcCover2(2)) → arcCoverB
  121. Rotate(arcCoverA, (-angleMoved), centerP2) → arcCoverA'
  122. Rotate(arcCoverB, (-angleMoved), centerP2) → arcCoverB'
  123. Rotate(dist1PN, pi / 2) → dist1PN'
  124. Polygon({centerP2, innerCenterInts(transClick), arcCover1(3), arcCover1(2)}) → polyCover1
  125. Polygon({innerCenterInts(transClick), centerP2, arcCover2(3), arcCover2(2)}) → polyCover2
  126. Rotate(polyCover1, (-angleMoved), centerP2) → polyCover1'
  127. Rotate(polyCover2, (-angleMoved), centerP2) → polyCover2'
  128. Polygon(DragPointNew, DragPointNew - dist1PN, DragPointNew - (dist1PN - dist1PN'), DragPointNew + dist1PN') → dragSquare2, dragpointnew, dragSquare2a, dragSquare2b, dragSquare2c
  129. Point(circleDrag) → PtDropped
  130. Circle(centerP2, innerCenterInts(transClick)) → innerCircle
  131. Circle(centerP2, If[α ≟ 90°, 1.3, 0.95]) → circleArrow
  132. Intersect(circleArrow, Ray[centerP2, CenterCircle]) → arrowCenter,
  133. Rotate(arrowCenter, -10°, centerP2) → arrowPoint1
  134. Rotate(arrowCenter, 10°, centerP2) → arrowPoint2
  135. CircleArc(centerP2, arrowPoint1, arrowPoint2) → arrowArc
  136. Vector(polyPoint(1), DragPoint) → transVect
  137. Element({arc1, arc2, arc3, arc4, arc1a, arc2a, arc3a, arc4a}, clickNum) → selectedArc
  138. If(clickNum ≟ 1, 8, clickNum ≟ 6, 2, clickNum ≟ 7, 2, clickNum ≟ 8, 1, 9, clickNum ≟ 2, 7, clickNum ≟ 3, 7, clickNum ≟ 4, 8, clickNum ≟ 5, 1) → thirdArcInd
  139. If(clickNum ≟ 1, 8, clickNum ≟ 6, 7, clickNum ≟ 7, 2, clickNum ≟ 8, 1, 9, clickNum ≟ 2, 7, clickNum ≟ 3, 2, clickNum ≟ 4, 1, clickNum ≟ 5, 8) → secondArcInd
  140. Segment(arrowCenter, arrowPoint1) → arrowSeg
  141. CircleSector(DragPoint + distCP, DragPoint - dist1, DragPoint - dist2) → staticDragArc1
  142. Angle(PolyA, centerP1, PolyB) → β
  143. Polygon(DragPoint, DragPoint + ((signDirectionX * 0.1), (signDirectionY * 0.1)), DragPoint + ((signDirectionX * 0.1), (signDirectionY * 0.8)), DragPoint + ((signDirectionX * 0.8), (signDirectionY * 0.8)), DragPoint + ((signDirectionX * 0.8), (signDirectionY * 0.1)), DragPoint + ((signDirectionX * 0.1), (signDirectionY * 0.1))) → dragSquareS, dragSquareS1, dragSquareS2, dragSquareS3, dragSquareS4, dragSquareS5, dragSquareS6
  144. If(clickNum ≤ 4, 5 - clickNum, 8 - Mod[clickNum, 5]) → clickSupp
  145. Element({arc1, arc2, arc3, arc4, arc1a, arc2a, arc3a, arc4a}, clickSupp) → arcSupp
  146. Rotate(PtArc1B, (-α), PtArc1C) → PtArc1A
  147. Rotate(PtArc2A, pi - α, PtArc2C) → PtArc2B
  148. CircleSector(PtArc2C, PtArc2A, PtArc2B) → arc2Sector
  149. CircleSector(PtArc1C, PtArc1A, PtArc1B) → arc1Sector
  150. Element({square1, square2, square3, square4, square1a, square2a, square3a, square4a}, clickSupp) → squareSupp
  151. Polygon(PtArc1C, PtArc1A, 4) → square1Sector, f, g, h, i, polyA, polyB
  152. Polygon(PtArc2C, PtArc2A, 4) → square2Sector, j, k, l, m, poly2A, poly2B
  153. If(clickNum < 4, 5 - clickNum, 9 - clickNum) → a
  154. Element({{(-0.58081, 0.43939), (-0.30718, 0.9), (-1.41919, 1.56061), (-1.69282, 1.1), (1.41919, -1.56061), (1.69282, -1.1), (0.58081, -0.43939), (0.30718, -0.9)}, {(0.43939, 0.58081), (1.69282, 0.9), (1.56061, 1.41919), (0.30718, 1.1), (-1.56061, -1.41919), (-0.30718, -1.1), (-0.43939, -0.58081), (-1.69282, -0.9)}, {(-0.1, 0.30718), (0.69282, 0.9), (0.1, 1.69282), (-0.69282, 1.1), (-0.1, -1.69282), (0.69282, -1.1), (0.1, -0.30718), (-0.69282, -0.9)}}, case - 1) → innerPoly1
  155. Element({{(-1.69282, 0.9), (-0.43939, 0.58081), (-0.30718, 1.1), (-1.56061, 1.41919), (0.30718, -1.1), (1.56061, -1.41919), (1.69282, -0.9), (0.43939, -0.58081)}, {(0.30718, 0.9), (0.58081, 0.43939), (1.69282, 1.1), (1.41919, 1.56061), (-1.69282, -1.1), (-1.41919, -1.56061), (-0.30718, -0.9), (-0.58081, -0.43939)}, {(-0.69282, 0.9), (0.1, 0.30718), (0.69282, 1.1), (-0.1, 1.69282), (-0.69282, -1.1), (0.1, -1.69282), (0.69282, -0.9), (-0.1, -0.30718)}}, case - 1) → innerPoly2
  156. If(x1 ≟ -1, 2, x1 ≟ 1, 3, 4) → caseN

AI Drawing Prompt Reference

Draw two parallel lines on a coordinate plane and add a transversal that intersects each parallel line at distinct points. At the two intersection points, form the angle pairs created by the transversal with each parallel line, and visually highlight a supplementary angle pair at/around one intersection using arc markers to show the angle regions. Include circular elements centered near the main intersection/corner points with fixed radii and a couple of circle-sector style arcs so the diagram clearly combines angle marking with standard geometric construction layout.
The prompt above was compiled from the original drawing commands and is for reference only.