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Pythagoras Theorem Model

Pythagoras Theorem Model
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2019-09-04 00:07
TriangleVectorGeometric Construction
This example illustrates the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Key concepts include right triangles and the Pythagorean Theorem. It is constructed using GeoGebra commands such as Intersect, Point, Polygon, etc. Suitable for middle school and above students to learn geometry and proof.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → C
  3. Polygon(A, C, 4) → poly3, n, p, q, r, H, I
  4. Point(xAxis) → B
  5. Polygon(B, A, 4) → poly2, j, k, l, m, F, G
  6. Polygon(A, B, C) → t1, c, a, b
  7. Polygon(C, B, 4) → poly1, f, g, h, i, D, E
  8. Line(I, i) → s
  9. Intersect(s, b) → K
  10. Segment(K, I) → e
  11. Line(A, h) → t
  12. Intersect(p, t) → J
  13. Segment(J, A) → d
  14. Intersect(d, e) → L
  15. Circle(B, Segment[J, L]) → d_1
  16. Intersect(d_1, a) → M,
  17. Polygon(J, L, K, C) → q1, j_1, l_1, k_1, c_1
  18. Polygon(K, L, A) → t2, a_1, k_2, l_2
  19. Polygon(L, I, A) → t3, a_2, l_3, i_1
  20. Polygon(H, J, L, I) → q2, h_1, j_2, l_4, i_2
  21. Vector(L, V) → u
  22. Translate(J, u) → J'
  23. Translate(L, u) → L'
  24. Translate(K, u) → K'
  25. Translate(C, u) → C'
  26. Polygon(J', L', K', C') → q1', j', l', k', c'
  27. Vector(L, W) → v
  28. Translate(K, v) → K'_1
  29. Translate(L, v) → L'_1
  30. Translate(A, v) → A'
  31. Polygon(K'_1, L'_1, A') → t2', a', k'_1, l'_1
  32. Vector(L, X) → w
  33. Translate(L, w) → L'_2
  34. Translate(I, w) → I'
  35. Translate(A, w) → A'_1
  36. Polygon(L'_2, I', A'_1) → t3', a'_1, l'_2, i'
  37. Vector(L, Y) → u_1
  38. Translate(H, u_1) → H'
  39. Translate(J, u_1) → J'_1
  40. Translate(L, u_1) → L'_3
  41. Translate(I, u_1) → I'_1
  42. Polygon(H', J'_1, L'_3, I'_1) → q2', h', j'_1, l'_3, i'_1
  43. Vector(F, Z) → v_1
  44. Translate(poly2, v_1) → poly2'