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Polygon Practice

Polygon Practice
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2024-01-24 16:01
PolygonGeometric Construction
In collections Deltoid - Flächeninhalt und Umkehraufgaben
This example demonstrates solving inverse problems related to quadrilaterals by transforming formulas. Key mathematical concepts include the properties of polygons and quadrilaterals. It uses commands/objects such as Midpoint, If, Element, SpeechBubbleLeft, Textfield, Polygon, PointIn, PolyLine, Angle, Point, Text, Segment in GeoGebra. Suitable for 7-8 grade students.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a quadrilateral and mark its four vertices. Then, find the midpoint of each side of the quadrilateral and connect these midpoints to form a new quadrilateral. Place a rectangle inside the original quadrilateral, ensuring its four vertices align with the midpoints of the quadrilateral's sides. Finally, draw a triangle outside the quadrilateral and label the key angles of both the quadrilateral and the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.