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Pythagorean Theorem (Right Triangles) Interactive Demo

Pythagorean Theorem (Right Triangles) Interactive Demo
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2020-05-15 03:21
TrianglePolygonAngleGeometric ConstructionSlider Animation
In collections Pythagorean Theorem
① This GeoGebra example demonstrates the Pythagorean theorem in a right triangle, showing that the sum of the squares of the two legs equals the square of the hypotenuse through an interactive geometric construction. ② Core mathematical concepts include the Pythagorean theorem, right triangles, area relationships, and algebraic-geometric verification. ③ Construction highlights: using GeoGebra commands such as Circle, Intersect, Segment, Rotate, Angle, Ray, Polygon, Textfield, and If to build the right triangle with attached squares, allowing dynamic input of side lengths and real-time verification; key objects include points A, B, C, segments a, b, c, and multiple text labels. ④ Suitable for middle school geometry classes to explore and prove the Pythagorean theorem, and also useful for high school math labs or introductory analytic geometry activities.

GeoGebra Commands & Parameters

  1. Circle(B, 6) → c
  2. Circle(A, 8) → c_1
  3. Intersect(c, c_1) → D, E, ,
  4. Segment(A, B) → f
  5. Segment(A, C) → g
  6. Rotate(A, (-β), B) → Α'
  7. Angle(Α', B, A) → β_1
  8. Segment(A, B) → q
  9. Segment(B, C) → r
  10. Angle(C, B, A) → γ
  11. Ray(B, Α') → s
  12. Intersect(c, s) → G,
  13. Polygon(G, B, 4) → πολύγ3, t, a_1, b, d, G_1, H
  14. Segment(B, C) → e
  15. Angle(B, A, C) → δ
  16. Angle(A, C, B) → ε
  17. Textfield(empty1) → ΕισΑΒ2
  18. Textfield(empty2) → ΕισAC2
  19. Textfield(empty3) → ΕισBC2
  20. Textfield(empty4) → ΕισBC
  21. Textfield(empty5) → ΕισAC2kaiBC2
  22. Polygon(B, A, 4) → πολύγ1, h, j, k, h_1, Α, Β
  23. SelectedElement(L) → text5
  24. SelectedIndex(L) → v
  25. SelectedIndex(L1) → w
  26. Point(c_1) → I
  27. Rotate(B, ζ, A) → B'
  28. Angle(B, A, B') → η
  29. Segment(A, B') → m
  30. Intersect(c_1, m) → J,
  31. Polygon(A, J, 4) → poly1, n, p, b_1, d_1, K, M
  32. Textfield(empty7) → ΕισαΑC
  33. Textfield(empty6) → ΕισΑΒ
  34. If(ans6 ≟ 10, true, false) → AB1
  35. If(ans1 ≟ 100, true, false) → AB2
  36. If(ans7 ≟ 8, true, false) → AC1
  37. If(ans2 ≟ 64, true, false) → AC2
  38. If(ans5 ≟ 100, true, false) → AC2kaiBC2
  39. If(ans3 ≟ 36, true, false) → BC2
  40. If(ans4 ≟ 6, true, false) → BC1

AI Drawing Prompt Reference

Draw a right triangle with squares on its two legs. Adjust the triangle's sides dynamically to show that the sum of the squares of the legs equals the square of the hypotenuse. Use circles and rotations to construct the square on the hypotenuse, labeling the lengths and areas to verify the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.