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Hinged Squares: A Visual Route to Pythagoras' Theorem

Hinged Squares: A Visual Route to Pythagoras' Theorem
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2019-11-13 03:45
TrianglePolygonAngleTransformationGeometric Construction
① This interactive GeoGebra construction demonstrates the Pythagorean theorem by hinging two squares on the sides of a right triangle, allowing dynamic rotation to reveal the area relationship. ② Core mathematical concepts include the Pythagorean theorem, its extension to the cosine rule, square area, right triangle side-angle relations, and symmetry. ③ Construction details: using GeoGebra commands such as Circle, Point, Line, OrthogonalLine, Intersect, Polygon, Segment, PointIn, and Angle, the applet builds a right triangle with squares on each side, connected by hinge points for rotation. ④ Suitable for middle and high school students, this resource supports inquiry-based learning of Pythagoras' theorem and can be extended to explore the cosine rule, bridging geometric intuition and algebraic proof.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Circle(A, C) → d
  3. Point(d) → D
  4. Line(A, D) → a
  5. OrthogonalLine(A, a) → b
  6. OrthogonalLine(D, a) → e
  7. Intersect(d, b, 2) → E
  8. OrthogonalLine(E, b) → f
  9. Intersect(e, f) → F
  10. Point(c) → G
  11. Line(A, G) → g
  12. OrthogonalLine(A, g) → h
  13. OrthogonalLine(G, g) → i
  14. Intersect(c, h, 1) → H
  15. OrthogonalLine(H, h) → j
  16. Intersect(i, j) → I
  17. Polygon(I, H, A, G) → poly1, i_1, h_1, a_1, g_1
  18. Polygon(A, E, F, D) → poly2, a_2, e_1, f_1, d_1
  19. Segment(D, G) → k
  20. OrthogonalLine(D, k) → l
  21. OrthogonalLine(G, k) → m
  22. Circle(D, G) → p
  23. Intersect(p, l, 2) → J
  24. OrthogonalLine(J, l) → n
  25. Intersect(m, n) → K
  26. Polygon(D, J, K, G) → poly3, d_2, j_1, k_1, g_2
  27. PointIn(poly3) → Pointpoly3
  28. Angle(G, A, D) → t

AI Drawing Prompt Reference

Draw a right triangle and construct squares on each of its sides. Connect the corresponding vertices of the two squares so they can hinge and rotate. Demonstrate that the sum of the areas of the two rotating squares equals the area of the square on the hypotenuse, visually proving the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.