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Inverse Problems - Triangles

Inverse Problems - Triangles
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2024-01-24 16:00
PolygonInequalityGeometric Construction
In collections Deltoid - Flächeninhalt und Umkehraufgaben
This example demonstrates how to solve inverse problems - triangles, particularly by transforming formulas to solve quadrilaterals. Students can explore the concept of inverse problems by adjusting the sides and angles of the triangles. The example involves core math concepts including geometry, polygons, and inverse problems. The construction points include using GeoGebra commands and objects such as Textfield, Shuffle, Polygon, etc. This example is suitable for 7-8 grade students, particularly those learning geometry and polygons.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Shuffle({1, 2}) → ModusList, {1, 2}
  3. Shuffle(Sequence[i, i, 3, 15]) → eList, {5, 12, 13, 9, 15, 14, 7, 8, 4, 10, 6, 3, 11}
  4. Shuffle({2, 4, 6, 8, 10, 12, 14} \ {ewert}) → fList, {14, 8, 12, 2, 4, 6}
  5. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  6. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {1, 3, 9, 7, 9, 3, 7, 8, 1, 3, 4, 6, 3, 4, 4, 10, 2, 6, 3, 5, 2, 3, 4, 8, 8, 0, 0, 2, 10, 4, 1, 6, 7, 10, 2, 6, 6, 5, 1, 8, 10, 8, 9, 7, 3, 4, 2, 1, 8, 10, 5, 2, 6, 10, 6, 10, 6, 3, 1, 10, 0, 6, 2, 10, 9, 9, 0, 10, 3, 6, 4, 0, 0, 9, 5, 4, 10, 2, 7, 4, 5, 3, 0, 1, 0, 7, 3, 4, 3, 9, 3, 1, 10, 9, 9, 9, 9, 7, 1, 3}
  7. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  8. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {8, 2, 2, 8, 8, 9, 0, 1, 6, 4, 1, 8, 1, 8, 6, 2, 4, 7, 0, 10, 9, 7, 0, 2, 2, 6, 10, 5, 6, 8, 9, 0, 5, 8, 4, 10, 7, 3, 7, 7, 7, 7, 5, 9, 4, 10, 9, 3, 1, 1, 4, 6, 3, 6, 6, 6, 0, 9, 8, 9, 4, 2, 1, 7, 0, 5, 2, 3, 6, 1, 10, 0, 1, 9, 9, 7, 3, 3, 0, 8, 10, 2, 0, 1, 2, 4, 5, 4, 9, 5, 6, 7, 0, 6, 5, 9, 9, 8, 9, 10}
  9. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  10. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  11. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  12. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  13. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  14. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  15. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  16. SelectedIndex(DD1) → index1
  17. TextToUnicode(erlaubteZeichen) → ZeichenLErlaubt
  18. TextToUnicode(Text[InputBox1]) → ZeichenLInput
  19. Polygon(B, C, D, E) → v1, b, c, d, e
  20. PointIn(v1) → TicketAnchor1
  21. Shuffle({1, 2, 3, 4, 5}) → TicketFarbenList, {4, 2, 1, 3, 5}
  22. SpeechBubbleRight(A, 9, 1.8) → Vieleck1

AI Drawing Prompt Reference

Construct a quadrilateral in the plane using four ordered points, connecting them to form a closed, rectangle-like shape. Use these four points as the polygon’s vertices and keep the vertex order consistent so the edges match correctly. Then place one additional anchor point inside the quadrilateral to serve as a reference for positioning. Finally, add a right-facing speech-bubble style label near the anchor point to indicate or explain the figure.
The prompt above was compiled from the original drawing commands and is for reference only.