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Angle World: Polygon Angle Calculation and Verification

Angle World: Polygon Angle Calculation and Verification
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2023-12-20 17:33
PolygonAngleGeometric ConstructionLocusGraphing
In collections Wiederholung Winkel: Bezeichnung, Arten, Messen & Zeichnen
This is an interactive angle practice tool that generates dynamic polygon problems for students to practice measuring and calculating various angles. Core mathematical concepts include: angle measurement and calculation, polygon interior and exterior angle relationships, and circle arc angle applications. Construction highlights: Uses Polygon command to draw random polygons, Angle command for automatic angle measurement, combines Text and Textfield for problem display and answer input, employs If and Validation logic for answer verification, tracks learning progress via attemptCount and correctCount. Suitable for middle school math classroom interactive practice or student self-review of angle-related knowledge.

GeoGebra Commands & Parameters

  1. Join(Sequence[Shuffle[Sequence[1, maxexnum]], m, 1, floor(110 / maxexnum)]) → listExNums
  2. Text(input1) → textinput1
  3. Textfield(input1) → InputBox1
  4. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  5. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {2, 10, 4, 5, 3, 4, 0, 6, 2, 9, 2, 0, 0, 10, 4, 1, 2, 9, 7, 0, 2, 5, 9, 5, 1, 5, 5, 8, 10, 3, 10, 10, 2, 5, 1, 1, 7, 6, 7, 2, 2, 0, 2, 8, 9, 5, 5, 2, 5, 0, 6, 0, 2, 9, 3, 5, 1, 10, 3, 6, 1, 0, 4, 0, 1, 8, 1, 4, 2, 1, 10, 2, 5, 2, 8, 7, 1, 6, 8, 6, 10, 5, 2, 8, 5, 0, 4, 3, 7, 1, 0, 1, 7, 8, 0, 3, 10, 9, 9, 5}
  6. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  7. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {3, 9, 5, 9, 10, 4, 8, 1, 4, 9, 9, 1, 2, 2, 2, 3, 6, 4, 9, 2, 0, 0, 1, 6, 9, 3, 1, 8, 3, 2, 3, 10, 10, 4, 7, 7, 5, 9, 6, 4, 4, 6, 9, 2, 0, 1, 1, 2, 10, 10, 3, 3, 3, 4, 3, 3, 1, 5, 5, 8, 2, 9, 2, 6, 5, 5, 9, 10, 3, 4, 3, 4, 2, 9, 9, 3, 8, 1, 10, 0, 0, 9, 2, 7, 5, 7, 9, 2, 2, 1, 8, 5, 8, 3, 7, 2, 3, 10, 8, 5}
  8. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  9. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  10. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  11. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  12. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  13. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  14. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  15. If(exnum ∈ {1, 2, 3}, "Neigungswinkel", If[exnum ∈ {4, 5, 6}, "Steigungswinkel", "Winkel"]) → winkelname
  16. If(exnum ∈ {1, 2, 3}, 620, If[exnum ∈ {4, 5, 6}, 626, 548]) → posInputBox
  17. Point(Line[B, xAxis]) → C
  18. Point(Line[D, xAxis]) → E
  19. Point(Line[P10a, xAxis]) → P10b
  20. Point(Line[P9a, xAxis]) → P9b
  21. Point(Line[P8a, xAxis]) → P8b
  22. Point(Line[P7a, xAxis]) → P7b
  23. Point(Line[P6a, xAxis]) → P6b
  24. Point(Line[P5a, xAxis]) → P5b
  25. Point(Line[P4a, xAxis]) → P4b
  26. Point(Line[P3a, xAxis]) → P3b
  27. Point(Line[P2a, xAxis]) → P2b
  28. Point(Line[P1a, xAxis]) → P1b
  29. Segment(F, (x(G), y(F))) → f
  30. Segment(F, G) → g
  31. Angle(F + (20, 0), F, G) → α
  32. Segment(H, (x(I), y(H))) → h
  33. Segment(H, I) → i
  34. Angle(H + (3, 0), H, I) → β
  35. Segment(J, (x(K), y(J))) → j
  36. Segment(J, K) → k
  37. Angle(J + (5, 0), J, K) → γ
  38. Segment(M, (x(L), y(M))) → l
  39. Segment(M, L) → m
  40. Angle(M + (-5, 0), M, L) → δ
  41. Segment(N, (x(O), y(N))) → n
  42. Segment(N, O) → p
  43. Angle(N + (10, 0), N, O) → ε
  44. Segment(P, (x(Q), y(P))) → q
  45. Segment(P, Q) → r
  46. Angle(Q, P, P + (-5, 0)) → ζ
  47. Segment(R, (x(S), y(R))) → s
  48. Segment(R, S) → t
  49. Angle(R + (10, 0), R, S) → η
  50. Segment(T, (x(U), y(T))) → a
  51. Segment(T, U) → b
  52. Angle(T + (10, 0), T, U) → θ
  53. Segment(V, W) → c
  54. Segment(V, (x(V), y(W))) → d
  55. Angle(W, V, V + (0, 10)) → ι
  56. Segment(A_1, B_1) → e
  57. Segment(A_1, C_1) → f_1
  58. Angle(B_1, A_1, C_1) → κ
  59. Point(c) → D_1
  60. Point(d) → E_1
  61. CircleArc(V, D_1, E_1) → c_1
  62. Point(f) → F_1
  63. CircleArc(F, F_1, G) → d_1
  64. Point(l) → G_1
  65. CircleArc(M, G_1, L) → e_1
  66. Defined(input1) → fixed
  67. SpeechBubbleRight(H_1, 8, 2.5) → Vieleck1
  68. Point(Line[J_1, xAxis]) → K_1
  69. Element({P1, P2, P3, P4, P5, P6, P7, P8, P9, P10}, exnum) → Pos
  70. SpeechBubbleRight(L_1, 5.8, 3) → Vieleck2
  71. Element({α, β, γ, δ, ε, ζ, η, θ, ι, κ}, exnum) → winkel

AI Drawing Prompt Reference

In one coordinate plane, draw a horizontal reference axis. Place four points on the plane to form a closed quadrilateral, connecting them in order to obtain a rectangle-like shape (top-left, top-right, bottom-right, bottom-left). Then choose several additional points and construct lines through pairs of points so each construction intersects the horizontal axis at its corresponding location. At each intersection vertex, draw two rays using one ray along a slightly horizontally shifted direction from the vertex and the other ray along the constructed line, forming multiple angles. Include the angle arc/angle marking and label angles with symbols such as α, β, γ, δ, ε, and ζ, and draw the corresponding line segments that define those rays. Keep all segments and angle labels visible and consistent with their shared vertex.
The prompt above was compiled from the original drawing commands and is for reference only.