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Proof Without Words

Proof Without Words
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2020-01-27 18:05
TriangleCoordinate GeometryGeometric Construction
Demonstrates the Pythagorean Theorem through dragging points and sliders. The example visually shows that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides using geometric transformations. GeoGebra commands used include point, polygon, mirror, rotate, translate, etc. Suitable for middle school and above students to learn geometric proofs.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Point(d) → E
  5. Midpoint(D, B) → F
  6. Mirror(E, F) → E'
  7. Rotate(E', 90°, F) → E''
  8. Mirror(E'', F) → E'''
  9. Polygon(A, E, E''') → poly2, e''', a_1, e
  10. Polygon(E, D, E'') → poly3, e'', e_1, d_1
  11. Polygon(E'', C, E') → poly4, e', e''_1, c_1
  12. Rotate(E'', (-((90° * f))), E'') → E'''_1
  13. Rotate(C, (-((90° * f))), E'') → C'
  14. Rotate(E', (-((90° * f))), E'') → E''_1
  15. Polygon(E'''_1, C', E''_1) → poly4', e''_2, e'''_2, c'
  16. Dilate(E''', 1 - f, B) → G
  17. Vector(E''', G) → u
  18. Translate(A, u) → A'
  19. Translate(E, u) → E'_1
  20. Translate(E''', u) → H
  21. Polygon(A', E'_1, H) → poly2', h, a', e'_2
  22. Circle(G, Segment[E'_1, A']) → g
  23. Intersect(g, b, 1) → I
  24. Circle(I, Segment[C', E'']) → k
  25. Circle(G, Segment[E''_1, E'']) → p
  26. Intersect(k, p, 2) → J
  27. Polygon(G, I, J) → poly5, j, g_1, i
  28. Segment(C, B) → l