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多边形练习题

多边形练习题
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2024-01-24 16:01
多边形几何作图
所属专题 Deltoid - Flächeninhalt und Umkehraufgaben
本范例演示了解四边形的逆向问题，通过变换公式来解决。涉及的核心数学概念包括多边形的性质和四边形的性质。使用了Midpoint, If, Element, SpeechBubbleLeft, Textfield, Polygon, PointIn, PolyLine, Angle, Point, Text, Segment等GeoGebra命令/对象进行构造。适合7-8年级的学生练习。

GeoGebra 命令及参数

  1. Midpoint(Corner[txtq321, 1], Corner[txtq321, 3]) → MP31
  2. Midpoint(Corner[txtq323, 1], Corner[txtq323, 3]) → MP33
  3. Midpoint(Corner[txtq322, 1], Corner[txtq322, 3]) → MP32
  4. If(questionCount ≟ 1, correctb1 ∧ correcte1 ∧ correctf1 ∧ correctdd11 ∧ correctdd12, questionCount ≟ 5, (¬option41) ∧ (¬option42) ∧ option43 ∧ (¬option44), false, questionCount ≟ 2, correcta2 ∧ correctdd21, questionCount ≟ 3 ∧ step3 ≟ 1, correct31, questionCount ≟ 3 ∧ step3 ≟ 2, correct321 ∧ correct322 ∧ correct323, questionCount ≟ 4, (¬option41) ∧ option42 ∧ option43 ∧ (¬option44)) → correct
  5. Element(randomQuestions, Mod[questionCount, Length[randomQuestions]] + 1) → randomQuestion
  6. Element(randomQuestions, questionCount) → actualQuestion
  7. If(step3 ≟ 1, 9.3, 10.25) → SB3width
  8. If(step3 ≟ 1, 2.25, 1.25) → SB3height
  9. SpeechBubbleLeft(SB0Point, SBwidthlist(questionCount + 1), SBheightlist(questionCount + 1)) → SB0
  10. Textfield(inputa1) → InputBoxa1
  11. Textfield(inputb1) → InputBoxb1
  12. Textfield(inputc1) → InputBoxc1
  13. Textfield(inputd1) → InputBoxd1
  14. Textfield(inpute1) → InputBoxe1
  15. Textfield(inputf1) → InputBoxf1
  16. Textfield(inputa2) → InputBoxa2
  17. Polygon(Corner[txtpos33, 1] + (-0.5, -2) + {(0, 0), (0, 6), (9, 6), (9, 0)}) → rectangle3
  18. PointIn(rectangle3) → Point31
  19. PolyLine({Corner[txtq321, 1], Corner[txtq321, 2], Corner[txtq321, 3], Corner[txtq321, 4], Corner[txtq321, 1]}) → seg321
  20. PolyLine({Corner[txtq322, 1], Corner[txtq322, 2], Corner[txtq322, 3], Corner[txtq322, 4], Corner[txtq322, 1]}) → seg322
  21. PolyLine({Corner[txtq323, 1], Corner[txtq323, 2], Corner[txtq323, 3], Corner[txtq323, 4], Corner[txtq323, 1]}) → seg323
  22. If(correctCount ≥ 5, (6.38, 2.6), (5, 2.6)) → PosBtnStartAgain
  23. Angle(Segment[(10.5, 5), (13.5, 5)], Segment[(12, 2), (12, 7)]) → deltoid53
  24. If(questionCount ≟ 1, Defined[inputb1] ∧ Defined[inpute1] ∧ Defined[inputf1] ∧ SelectedIndex[dropdown11] ≠ 1 ∧ SelectedIndex[dropdown12] ≠ 1, questionCount ≟ 5, option41 ∨ option42 ∨ option43 ∨ option44, true, questionCount ≟ 2, Defined[inputa2] ∧ SelectedIndex[dropdown21] ≠ 1 ∧ isCalculated, questionCount ≟ 3 ∧ step3 ≟ 1, selectedq31 ∨ selectedq32 ∨ selectedq33, questionCount ≟ 3 ∧ step3 ≟ 2, Sort[{PosP031, PosP032, PosP033}] ≟ Sort[{PosDD031, PosDD032, PosDD033}], questionCount ≟ 4, CountIf[a ≟ true, a, {option41, option42, option43, option44}] ≟ 2) → clickableBtnValidate
  25. Angle((11.5, 7), (11.5, 5), (10, 5)) → rightAngle4
  26. Point(Line[A, xAxis]) → B
  27. Text(txtq321, PosP031 + (0, 0.05), false, true, 0, 0) → txtDD031
  28. Text(txtq322, PosP032 + (0, 0.05), false, true, 0, 0) → txtDD032
  29. Text(txtq323, PosP033 + (0, 0.05), false, true, 0, 0) → txtDD033
  30. Text("\textsf{\textcolor{#50c1ce}{\bold{Zieh mich!}}", Midpoint[ParkP031, ParkP033] + (-1.25, 0), false, true, 0, 0) → CapZiehMich03
  31. Segment(Midpoint[Corner[CapZiehMich03, 4], Corner[CapZiehMich03, 3]], Midpoint[Corner[CapZiehMich03, 4], Corner[CapZiehMich03, 3]] + (0.2 * Vector[Midpoint[Corner[CapZiehMich03, 4], Corner[CapZiehMich03, 3]], PosP031])) → seg0321
  32. Segment(Midpoint[Corner[CapZiehMich03, 2], Corner[CapZiehMich03, 1]], Midpoint[Corner[CapZiehMich03, 2], Corner[CapZiehMich03, 1]] + (0.2 * Vector[Midpoint[Corner[CapZiehMich03, 1], Corner[CapZiehMich03, 2]], PosP033])) → seg0323
  33. Segment(Midpoint[Corner[CapZiehMich03, 2], Corner[CapZiehMich03, 3]], Midpoint[Corner[CapZiehMich03, 2], Corner[CapZiehMich03, 3]] + (0.2 * Vector[Midpoint[Corner[CapZiehMich03, 3], Corner[CapZiehMich03, 2]], PosP032])) → seg0322

AI 绘图提示语参考

画一个四边形，并标记出四边形的四个顶点。然后，找到四边形每条边的中点，并连接这些中点形成一个新的四边形。在四边形内部放置一个矩形，并确保矩形的四个顶点分别位于四边形四条边的中点位置。最后，在四边形外部绘制一个三角形，并标注出四边形和三角形的关键角度。
以上提示语为根据原始绘图命令整理而来，仅供参考。