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Pythagorean Theorem for Obtuse Triangles with Irrational Sides

Pythagorean Theorem for Obtuse Triangles with Irrational Sides
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2020-05-15 03:30
TriangleCoordinate GeometryGeometric Construction
In collections Pythagorean Theorem
This example demonstrates the Pythagorean Theorem for obtuse triangles with irrational side lengths. It explores the relationship between the hypotenuse and the legs of an obtuse triangle by constructing a right triangle and showing that the square of the hypotenuse equals the sum of the squares of the legs. The construction uses commands such as line segment, point, angle, and intersection in GeoGebra. Suitable for middle school and above students to learn geometric construction and the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Segment(A_1, B_1) → f
  2. Segment(A_1, B_1) → q
  3. Textfield(empty1) → ΕισΑΒ2
  4. Textfield(empty2) → ΕισAC2
  5. Textfield(empty3) → ΕισBC2
  6. Textfield(empty5) → ΕισAC2kaiBC2
  7. SelectedElement(L) → text5
  8. SelectedIndex(L) → v
  9. SelectedIndex(L1) → w
  10. Polygon(C, A, B) → poly1, b, c, a_1
  11. Angle(poly1) → α, β, γ
  12. Polygon(A, C, 4) → poly2, d, e, g, h, D, E
  13. Polygon(C, B, 4) → poly3, i, j, k, l, F, G
  14. Polygon(B, A, 4) → poly4, m, n, p, r, H, I
  15. Segment(J, A) → a
  16. Point(a) → K
  17. Intersect(n, p) → M
  18. Segment(K, M) → s
  19. Point(s) → N
  20. Intersect(p, r) → O
  21. Segment(N, O) → t
  22. Point(t) → P
  23. Point(r) → Q
  24. Segment(P, Q) → b_1
  25. Intersect(g, h) → T
  26. Point(g) → U
  27. Intersect(k, l) → V
  28. Point(k) → W
  29. Segment(M, R) → e_1
  30. Segment(A, S) → f_1
  31. Segment(Z, B) → g_1
  32. Point(e_1) → C_1
  33. Segment(O, C_1) → h_1
  34. Segment(A, D_1) → i_1
  35. Point(i_1) → E_1
  36. Segment(T, E_1) → k_1
  37. If(ans1 ≟ 37, true, false) → AB2
  38. Segment(U, F_1) → j_1
  39. Point(j_1) → G_1
  40. Intersect(e, l) → H_1
  41. Segment(G_1, H_1) → l_1
  42. Segment(H_1, J_1) → d_1
  43. Point(d_1) → K_1
  44. Segment(G, K_1) → m_1
  45. Point(m_1) → L_1
  46. Segment(L_1, W) → n_1
  47. Point(n_1) → M_1
  48. Segment(I_1, M_1) → c_1
  49. If(ans2 ≟ 13, true, false) → AC2
  50. If(ans5 ≟ 33, true, false) → AC2kaiBC2
  51. If(ans3 ≟ 20, true, false) → BC2