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Pythagorean Theorem with Irrational Sides

Pythagorean Theorem with Irrational Sides
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2020-05-15 03:28
TriangleFunctionGeometric Construction
This example demonstrates the Pythagorean Theorem in right triangles with irrational side lengths. Key mathematical concepts include the theorem, trigonometric functions, and geometric construction. The construction uses GeoGebra commands such as Segment, Polygon, Angle, and Intersect to create triangles and calculate side lengths. Suitable for high school students or math enthusiasts learning geometric principles and tool usage.

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. If(ans1 ≟ 16, true, false) → AB2
  16. If(ans2 ≟ 8, true, false) → AC2
  17. If(ans5 ≟ 16, true, false) → AC2kaiBC2
  18. If(ans3 ≟ 8, true, false) → BC2
  19. Segment(J, A) → a
  20. Point(a) → K
  21. Intersect(n, p) → M
  22. Segment(K, M) → s
  23. Point(s) → N
  24. Intersect(p, r) → O
  25. Segment(N, O) → t
  26. Point(t) → P
  27. Point(r) → Q
  28. Segment(P, Q) → b_1