MathPlotAI Logo MathPlotAI

Visual Proof of Pythagorean Theorem using Geometric Transformations

Visual Proof of Pythagorean Theorem using Geometric Transformations
Loading the math board and drawing, please wait…
2016-07-11 14:38
TrianglePolygonTransformationGeometric Construction
This GeoGebra applet provides a visual proof of the Pythagorean theorem. It demonstrates the relationship between the squares of the sides of a right triangle through geometric dissection and rotation. Key concepts include the Pythagorean theorem, area conservation, and rigid transformations. Construction utilizes commands such as Line, Polygon, Rotate, Intersect, and OrthogonalLine to create dynamic geometric figures. Ideal for high school geometry students and educators seeking interactive teaching tools to illustrate fundamental mathematical principles.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Point(a) → C
  3. OrthogonalLine(A, a) → b
  4. Point(b) → D
  5. Polygon(D, A, C) → poly1, c, d, a_1
  6. Midpoint(A, E) → F
  7. Rotate(D, α, F) → D'
  8. Rotate(A, α, F) → A'
  9. Rotate(C, α, F) → C'
  10. Polygon(D', A', C') → poly1', c', d', a'
  11. Point(b) → G
  12. Point(d) → J
  13. Polygon(A, G, E, J) → poly4, a_2, g_1, e_1, j
  14. Polygon(D, G, H) → poly2, h, d_1, g
  15. Polygon(H, E, I) → poly3, i, h_1, e
  16. Segment(D, H) → r
  17. Circle(D, p) → f
  18. Intersect(f, g, 1) → K
  19. Intersect(f, a_1, 1) → L
  20. Polygon(L, M, N) → poly5, n, l, m
  21. Polygon(K, O, P) → poly6, p_1, k, o
  22. Midpoint(K, O) → Q
  23. Midpoint(O, P) → R
  24. Polygon(H, O, 4) → poly7, h_2, o_1, q, s, S, U
  25. Polygon(M, C, 4) → poly8, m_1, c_1, t, b_1, V, W