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Pythagorean Theorem Demo by Vladimiro González Zelaya

Pythagorean Theorem Demo by Vladimiro González Zelaya
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2015-09-15 04:46
TriangleCoordinate GeometryGeometric Construction
This example dynamically demonstrates the Pythagorean theorem by visualizing the relationship between the sides of a right triangle. Key math concepts include the Pythagorean theorem, right triangles, and coordinate geometry. Construction highlights the use of commands like Intersect, Polygon, Circle, OrthogonalLine, Line, PointIn, Segment, and Angle. Suitable for middle school and above mathematics education to aid comprehension of the theorem and its applications.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → C_1
  2. Polygon(C_1, A_1, B_1) → poly1, b_1, c, a_1
  3. Circle(C_1, b_1) → d
  4. Intersect(d, yAxis, 1) → D
  5. OrthogonalLine(D, yAxis) → e
  6. OrthogonalLine(A_1, b_1) → f
  7. Intersect(e, f) → E
  8. Polygon(C_1, D, E, A_1) → ASquare, c_1, d_1, e_1, A
  9. OrthogonalLine(B_1, c) → g
  10. OrthogonalLine(A_1, c) → h
  11. Circle(A_1, c) → k
  12. Intersect(k, h, 1) → F
  13. OrthogonalLine(F, h) → i
  14. Intersect(g, i) → G
  15. Polygon(B_1, A_1, F, G) → CSquare, C, a_3, f_1, g_1
  16. Line(B_1, xAxis) → j
  17. Circle(B_1, a_1) → p
  18. Circle(C_1, a_1) → q
  19. Intersect(p, j, 1) → H
  20. Intersect(q, xAxis, 1) → I
  21. Polygon(B_1, H, I, C_1) → BSquare, b_3, h_1, i_1, B
  22. PointIn(CSquare) → Pointpoly3
  23. PointIn(ASquare) → Pointpoly2
  24. PointIn(BSquare) → Pointpoly4
  25. Intersect(c_1, d_1) → J
  26. Intersect(b_1, c) → K
  27. Segment(J, K) → l
  28. Intersect(b_1, a_1) → L
  29. Intersect(d_1, e_1) → M
  30. Segment(L, M) → m
  31. Intersect(l, m) → N
  32. Angle(A_1, C_1, B_1) → α