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Pythagorean Theorem and Triangle Construction

Pythagorean Theorem and Triangle Construction
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2020-05-15 03:26
TriangleCircleAngleGeometric Construction
This example demonstrates the Pythagorean Theorem in right-angled triangles, showing the relationship between the sides through dynamic construction. Key math concepts include the Pythagorean Theorem, circles, triangles, and angle measurement. GeoGebra commands and objects used in the construction are Circle (draw circle), Intersect (intersection points), Segment (line segments), Rotate (rotation), Angle (angle measurement), Ray (ray), Polygon (polygons), and Textfield (text fields). Suitable for middle school students and above for learning geometric constructions and theorem verification, as well as high school mathematics teaching demonstrations.

GeoGebra Commands & Parameters

  1. Circle(B, 7) → c
  2. Circle(A, 5) → 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 ≟ 5, true, false) → AC1
  37. If(ans2 ≟ 25, true, false) → AC2
  38. If(ans5 ≟ 84, true, false) → AC2kaiBC2
  39. If(ans4 ≟ 7, true, false) → BC1
  40. If(ans3 ≟ 49, true, false) → BC2