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Pythagorean Theorem for Acute Triangles with Irrational Sides

Pythagorean Theorem for Acute Triangles with Irrational Sides
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2020-05-15 03:29
TriangleCoordinate GeometryGeometric Construction
In collections Pythagorean Theorem
This example demonstrates the Pythagorean theorem for acute triangles, involving irrational side lengths. Using GeoGebra commands such as Segment, Textfield, Polygon, etc., it illustrates the application of the Pythagorean theorem in acute triangles. 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(C, W) → c_1
  30. Segment(B, V) → d_1
  31. Segment(M, R) → e_1
  32. Segment(A, S) → f_1
  33. Segment(Z, B) → g_1
  34. Point(e_1) → C_1
  35. Segment(O, C_1) → h_1
  36. Segment(A, D_1) → i_1
  37. Point(i_1) → E_1
  38. Segment(T, E_1) → k_1
  39. Point(k_1) → F_1
  40. Segment(F_1, U) → l_1
  41. Point(l_1) → G_1
  42. Segment(G_1, C) → j_1
  43. If(ans1 ≟ 37, true, false) → AB2
  44. If(ans2 ≟ 25, true, false) → AC2
  45. If(ans5 ≟ 43, true, false) → AC2kaiBC2
  46. If(ans3 ≟ 18, true, false) → BC2