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Find the Hypotenuse Using the Pythagorean Theorem

Find the Hypotenuse Using the Pythagorean Theorem
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2024-09-26 21:28
TriangleAngleTrigonometryGeometric Construction
In collections Satz des Pythagoras - Einführung
This GeoGebra activity lets students enter the two legs of a right triangle and then computes and checks the hypotenuse length, emphasizing practical calculation (with a calculator) and step-by-step validation. The central math concepts are the Pythagorean Theorem (a² + b² = c²), forming the correct equation for an unknown side length, and applying it within a planar right-triangle setting. Construction and interaction rely on GeoGebra commands/objects such as Sequence for generating random values and tracking attempts, Point and Polygon to build the right triangle, Angle to enforce the right-angle relationship, and Textfield with If to handle user input, validate it, and present feedback. It is well suited for grades 7–8 as guided practice for applying formulas in plane geometry.

GeoGebra Commands & Parameters

  1. Sequence(Random[10, 1000] / 10, i, 1, 100) → randomNumbersA, {17.1, 19.1, 82.8, 11, 74.3, 20.9, 12.6, 32.6, 22.6, 14.4, 63.9, 30.7, 49.8, 96, 49, 3.6, 30.9, 75.3, 61.2, 50.8, 77.2, 25, 35, 16.8, 16, 72.4, 19.5, 29.4, 87.1, 55.2, 62.1, 1.5, 60.2, 74.7, 43, 68.6, 22.5, 15.9, 98, 93.6, 40.3, 99, 68.2, 87.9, 91.1, 55, 79.3, 12.1, 52.4, 90.5, 87, 20.3, 24.3, 27.1, 52.9, 73, 19.5, 63, 64.1, 78.2, 48.2, 22.6, 82.4, 1.5, 6.1, 47.3, 37.1, 21.3, 38.8, 2.7, 53.2, 17.3, 83.1, 33.6, 15.7, 3.9, 24.1, 73.6, 97.2, 65.9, 98.6, 7.4, 27, 26, 91.9, 29.8, 89.5, 52.5, 7.2, 3.6, 78.9, 13.6, 6.5, 15.3, 56.7, 28.2, 16.9, 69.3, 31.5, 29.3}
  2. Element(randomNumbersA, Mod[questionCount, Length[randomNumbersA]] + 1) → randomNumberA
  3. Sequence(Random[If[floor((randomNumbersA(i) * 0.3)) > 1, (floor((randomNumbersA(i) * 0.3)) * 10), 10], If[ceil((randomNumbersA(i) * 1.7)) < 100, (ceil((randomNumbersA(i) * 1.7)) * 10), 1000]] / 10, i, 1, 100) → randomNumbersB, {27.4, 14.4, 62.7, 11.2, 99.7, 27.9, 8.6, 13.6, 8.4, 15.8, 77.3, 36.1, 37.9, 65, 24.3, 5.7, 38, 54, 54.6, 25.9, 70.1, 8.3, 38.6, 26.2, 23.6, 33.4, 28.7, 19.9, 57, 54.4, 57.9, 1.7, 62.7, 80.1, 59.6, 77.2, 10, 25.6, 95.3, 86.2, 66.4, 66.4, 58, 39.4, 58.1, 73.7, 94.5, 19.6, 82.2, 95.9, 46.1, 22, 21.3, 21.8, 34.2, 43.6, 27.5, 66.1, 74.8, 79.7, 50.7, 35.6, 57.8, 2.2, 6.6, 37.2, 53.6, 13.5, 64.5, 1.8, 30.8, 15.2, 32.7, 50.3, 27, 6.6, 8.8, 98.8, 70.6, 66.5, 59.7, 6.8, 32.3, 34.8, 30.5, 43.8, 94, 81.4, 5.9, 3.4, 40, 21.8, 1.4, 21.6, 29.5, 41.8, 22.2, 49.5, 27.7, 20.8}
  4. Element(randomNumbersB, Mod[questionCount, Length[randomNumbersB]] + 1) → randomNumberB
  5. Textfield(input) → inputBox
  6. If(Length[Text[inputBox]] > 0, Length[KeepIf[¬(temp ∈ TextToUnicode[erlaubteZeichen]), temp, Take[TextToUnicode[Text[inputBox]], Min[Length[Text[inputBox]], 2]]]] ≟ 0, true) → inputValid
  7. Polygon(dreieckStartA, dreieckStartB, dreieckStartC) → dreieckStart, dreieckStartc, dreieckStarta, dreieckStartb
  8. Angle(dreieckStartA, dreieckStartC, dreieckStartB) → dreieckStartGamma
  9. Angle(dreieckStartB, dreieckStartA, dreieckStartC) → dreieckStartAlpha
  10. Angle(dreieckStartC, dreieckStartB, dreieckStartA) → dreieckStartBeta
  11. Point(Circle[dreieckSolutionC, (randomNumberA * dreieckFactor)]) → dreieckSolutionA
  12. Polygon(dreieckSolutionC, dreieckSolutionA, dreieckSolutionB) → dreieck1, dreieckSolutionb, dreieckSolutionc, dreieckSolutiona
  13. Angle(dreieckSolutionB, dreieckSolutionA, dreieckSolutionC) → dreieckSolutionAlpha
  14. Angle(dreieckSolutionA, dreieckSolutionC, dreieckSolutionB) → dreieckSolutionGamma
  15. Angle(dreieckSolutionC, dreieckSolutionB, dreieckSolutionA) → dreieckSolutionBeta
  16. Flatten(Sequence[Shuffle[{"mm", "cm", "dm", "m"}], i, 1, 10]) → randomUnits
  17. Element(randomUnits, Mod[questionCount, Length[randomUnits]] + 1) → randomUnit

AI Drawing Prompt Reference

Draw a right triangle with the lengths of the two legs being 17.1 and 27.4 units respectively. Use the Pythagorean theorem to calculate the length of the hypotenuse and enter the result in the input box. If the input is correct, show a correct message; otherwise, show an incorrect message.
The prompt above was compiled from the original drawing commands and is for reference only.