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Pythagorean Theorem in Obtuse Triangles

Pythagorean Theorem in Obtuse Triangles
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2020-05-15 03:26
TriangleAngleTrigonometryOptimizationGeometric Construction
In collections Pythagorean Theorem
This example demonstrates the Pythagorean theorem in obtuse triangles. Key mathematical concepts include triangles, angles, and the Pythagorean theorem. Using GeoGebra commands such as Circle, Intersect, Segment, etc., the construction of an obtuse triangle and verification of the Pythagorean theorem are shown. Suitable for middle school and above students learning geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Circle(B, 10) → c
  2. Circle(A, 7) → 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 ≟ 14, true, false) → AB1
  35. If(ans1 ≟ 196, true, false) → AB2
  36. If(ans7 ≟ 7, true, false) → AC1
  37. If(ans2 ≟ 49, true, false) → AC2
  38. If(ans5 ≟ 149, true, false) → AC2kaiBC2
  39. If(ans4 ≟ 10, true, false) → BC1
  40. If(ans3 ≟ 100, true, false) → BC2