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Pythagoras' Theorem Demonstration by GreenMaths

Pythagoras' Theorem Demonstration by GreenMaths
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2014-02-17 00:27
TriangleCoordinate GeometryGeometric Construction
In collections Pythagoras
This example demonstrates Pythagoras' theorem using lengths. It involves the core mathematical concept of Pythagoras' theorem. Using GeoGebra commands such as Point, Intersect, Midpoint, Circle, etc., a right triangle is constructed to verify the theorem. Suitable for middle school and above students to learn geometry and algebra.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Intersect(xAxis, yAxis) → A
  3. Midpoint(A, B) → O
  4. Circle(O, B) → o
  5. Point(o) → C
  6. Rotate(C, 90*°, A) → D
  7. Rotate(A, 270*°, C) → E
  8. Line(D, E) → m
  9. Vector(D, E) → v_b
  10. Length(v_b) → k_b
  11. Rotate(C, 270*°, B) → F
  12. Rotate(B, 90*°, C) → G
  13. Line(F, G) → n
  14. Intersect(m, n) → H
  15. Line(H, yAxis) → hc
  16. Vector(E, H) → u_a
  17. Length(u_a) → ku_b
  18. Vector(G, H) → u_b
  19. Length(u_b) → ku_a
  20. Vector(F, G) → v_a
  21. Length(v_a) → k_a
  22. Rotate(B, 270*°, A) → I
  23. Vector(A, I) → v_c
  24. Length(v_c) → k_c
  25. Circle(H, ku_a * ku_b / k_c) → d
  26. Intersect(d, hc) → K, L
  27. Vector(H, L) → v_h
  28. Rotate(A, 90*°, B) → J
  29. If(a < ka_1, Point[F, Vector[a / ka_1 * u_b]], If[a < ka_2, Point[F, u_b], Point[F, Vector[u_b + (a - ka_2) / (1 - ka_2) * v_c]]]) → F'
  30. Polygon(B, C, G, F) → P, b_1, c, g, f
  31. If(a < ka_1, Point[G, Vector[a / ka_1 * u_b]], If[a < ka_2, Point[H, Vector[(a - ka_1) / (ka_2 - ka_1) * v_h]], Point[L, Vector[(a - ka_2) / (1 - ka_2) * v_c]]]) → G'
  32. If(a < ka_1, C, If[a < ka_2, Point[C, Vector[(a - ka_1) / (ka_2 - ka_1) * v_h]], Point[C, Vector[v_h + (a - ka_2) / (1 - ka_2) * v_c]]]) → Ca'
  33. Vector(G', Ca') → u
  34. If(a < ka_1, B, If[a < ka_2, B, Point[B, Vector[(a - ka_2) / (1 - ka_2) * v_c]]]) → B'
  35. Vector(F', B') → v
  36. Polygon(B', Ca', G', F') → Q, b', c', g', f'
  37. If(b < kb_1, Point[E, Vector[b / kb_1 * u_a]], If[b < kb_2, Point[H, Vector[(b - kb_1) / (kb_2 - kb_1) * v_h]], Point[L, Vector[(b - kb_2) / (1 - kb_2) * v_c]]]) → E'
  38. If(b < kb_1, Point[D, Vector[b / kb_1 * u_a]], If[b < kb_2, Point[D, u_a], Point[D, Vector[u_a + (b - kb_2) / (1 - kb_2) * v_c]]]) → D'
  39. If(b < kb_1, C, If[b < kb_2, Point[C, Vector[(b - kb_1) / (kb_2 - kb_1) * v_h]], Point[C, Vector[v_h + (b - kb_2) / (1 - kb_2) * v_c]]]) → Cb'
  40. If(b < kb_1, A, If[b < kb_2, A, Point[A, Vector[(b - kb_2) / (1 - kb_2) * v_c]]]) → A'
  41. Polygon(A, C, E, D) → R, a_1, c_1, e, d_1
  42. Polygon(A', Cb', E', D') → S, a', cb', e', d'
  43. Polygon(A, B, J, I) → T, a_2, b_2, j, i
  44. Angle(A, C, B) → α
  45. Midpoint(C, B) → M
  46. Midpoint(A, C) → N

AI Drawing Prompt Reference

Draw a right triangle ABC with A on the x-axis, B at the origin, and C on circle O. Construct another right triangle DEF with D, E, F on circle O through rotation and intersection. Adjust the positions of the points to verify the Pythagorean theorem, i.e., AB² + BC² = AC².
The prompt above was compiled from the original drawing commands and is for reference only.