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Mixed Tasks - Deltoid

Mixed Tasks - Deltoid
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2024-07-10 20:52
PolygonAngleGeometric Construction
In collections Deltoid - Flächeninhalt und Umkehraufgaben
This example demonstrates the construction and properties of a deltoid. Key math concepts include polygons, angle calculations, and formula manipulation. GeoGebra commands and objects used in the construction are Join, Sequence, Element, Zip, If, Segment, Textfield, Polygon, Append, Remove, Intersect, Angle, NumberSeparationComma, Text. Suitable for 7-8 grade students to practice solving inverse problems related to quadrilaterals.

GeoGebra Commands & Parameters

  1. Join({Sequence[1, 15], {20, 30, 40, 50}}) → listPool
  2. Sequence(RandomElement[listPool], m, 1, 110) → randomNosForX, {1, 30, 11, 11, 8, 15, 20, 7, 14, 4, 30, 7, 3, 5, 3, 6, 13, 11, 9, 1, 50, 1, 30, 9, 5, 1, 8, 10, 11, 9, 30, 14, 8, 11, 8, 14, 15, 1, 13, 3, 14, 15, 13, 50, 12, 1, 40, 30, 2, 40, 50, 14, 10, 6, 7, 4, 4, 15, 12, 2, 30, 12, 6, 1, 15, 7, 1, 30, 8, 8, 40, 14, 6, 10, 11, 8, 6, 8, 1, 1, 7, 11, 10, 12, 50, 15, 11, 40, 2, 1, 15, 9, 8, 40, 15, 9, 12, 40, 2, 40, 20, 11, 8, 7, 14, 50, 5, 14, 10, 5}
  3. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  4. Zip(RandomElement[listPool \ Join[{{m}, Sequence[1, (floor(m) * (1 - percentage))], Sequence[(ceil(m) * (1 + percentage)), 50]}]], m, randomNosForX) → randomNosForY
  5. If(Defined[numYrandom], numYrandom, floor((numX * 1.5))) → numY
  6. If(numX ≥ numY, P1, P5) → A
  7. If(numX ≥ numY, P3, P7) → C
  8. Segment(A, C) → e1
  9. Sequence(RandomElement[Sequence[0.3, 0.5, 0.01]], m, 1, 110) → randomNosForProp, {0.38000000000000006, 0.31, 0.32, 0.32, 0.3, 0.35000000000000003, 0.47000000000000014, 0.48000000000000015, 0.31, 0.5000000000000001, 0.39000000000000007, 0.35000000000000003, 0.4100000000000001, 0.47000000000000014, 0.37000000000000005, 0.48000000000000015, 0.3, 0.35000000000000003, 0.3, 0.47000000000000014, 0.47000000000000014, 0.4500000000000001, 0.38000000000000006, 0.34, 0.33, 0.38000000000000006, 0.48000000000000015, 0.36000000000000004, 0.46000000000000013, 0.3, 0.4300000000000001, 0.4300000000000001, 0.46000000000000013, 0.4200000000000001, 0.32, 0.36000000000000004, 0.34, 0.36000000000000004, 0.3, 0.37000000000000005, 0.31, 0.32, 0.46000000000000013, 0.4100000000000001, 0.34, 0.34, 0.37000000000000005, 0.4200000000000001, 0.4100000000000001, 0.38000000000000006, 0.46000000000000013, 0.3, 0.4400000000000001, 0.4500000000000001, 0.4100000000000001, 0.4400000000000001, 0.38000000000000006, 0.33, 0.4000000000000001, 0.46000000000000013, 0.4400000000000001, 0.3, 0.46000000000000013, 0.4500000000000001, 0.38000000000000006, 0.4300000000000001, 0.5000000000000001, 0.4100000000000001, 0.31, 0.37000000000000005, 0.4000000000000001, 0.48000000000000015, 0.47000000000000014, 0.31, 0.4500000000000001, 0.35000000000000003, 0.4200000000000001, 0.36000000000000004, 0.36000000000000004, 0.49000000000000016, 0.4500000000000001, 0.4400000000000001, 0.39000000000000007, 0.47000000000000014, 0.4500000000000001, 0.4100000000000001, 0.5000000000000001, 0.36000000000000004, 0.47000000000000014, 0.47000000000000014, 0.48000000000000015, 0.49000000000000016, 0.35000000000000003, 0.32, 0.3, 0.49000000000000016, 0.33, 0.5000000000000001, 0.4100000000000001, 0.3, 0.34, 0.32, 0.4000000000000001, 0.48000000000000015, 0.37000000000000005, 0.35000000000000003, 0.36000000000000004, 0.4100000000000001, 0.4400000000000001, 0.49000000000000016}
  10. If(numX ≥ numY, P4, P8) → D
  11. If(numX ≥ numY, P2, P6) → B
  12. Segment(B, D) → f1
  13. Join(Sequence[Shuffle[{1, 2, 3}], k, 1, 34]) → CaseList
  14. If(Case ≟ 1, numX, Case ≟ 2, numY, numZ) → sol
  15. Textfield(input1) → InputBox1
  16. Textfield(input2) → InputBox2
  17. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  18. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  19. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  20. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  21. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  22. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  23. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  24. Intersect(e1, f1) → E
  25. Angle(A, E, D) → α
  26. NumberSeparationComma((numX * numY)) → numberSeparationZaehler
  27. Text("\scriptsize{\textsf{Skizze ist maßstabsgetreu}}", C + (0, -0.6), false, true, 0, -1) → txtSkizze

AI Drawing Prompt Reference

Draw a deltoid by first creating two line segments e1 and f1, connecting points A and C, and B and D respectively. The coordinates of A, B, C, and D are generated randomly to satisfy the deltoid's properties. Then, find the intersection point E of e1 and f1, and calculate angle α. Finally, create a rectangle based on given x and y values, ensuring the rectangle matches the size of the deltoid.
The prompt above was compiled from the original drawing commands and is for reference only.