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Pythagorean Theorem Demonstration by Mary Anne Ward

Pythagorean Theorem Demonstration by Mary Anne Ward
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2014-03-15 10:54
TriangleTrigonometryCoordinate GeometryGeometric ConstructionSlider Animation
This applet demonstrates the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Key concepts include right-angled triangles and the Pythagorean Theorem. Using GeoGebra commands such as Segment, OrthogonalLine, and Circle, the applet dynamically shows the relationship between the sides of a right-angled triangle. Suitable for middle school and above students learning geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Segment(C, A) → c
  5. Segment(C, B) → d
  6. Circle(C, B) → e
  7. OrthogonalLine(C, d) → f
  8. Intersect(e, f, 2) → D
  9. Segment(D, C) → g
  10. OrthogonalLine(B, d) → h
  11. OrthogonalLine(D, g) → i
  12. Intersect(h, i) → E
  13. Segment(E, B) → j
  14. Segment(E, D) → k
  15. Polygon(C, D, E, B) → poly1, c_1, d_1, e_1, b_1
  16. PointIn(poly1) → Pointpoly1
  17. Circle(A, B) → p
  18. OrthogonalLine(A, a) → l
  19. Intersect(p, l, 1) → F
  20. Circle(B, A) → q
  21. OrthogonalLine(B, a) → m
  22. Intersect(q, m, 1) → G
  23. OrthogonalLine(G, m) → n
  24. Line(A, F) → r
  25. Segment(A, F) → s
  26. Segment(F, G) → t
  27. Segment(G, B) → a_1
  28. Polygon(A, B, G, F) → poly2, a_2, b_2, g_1, f_1
  29. PointIn(poly2) → Pointpoly2
  30. Circle(C, A) → h_1
  31. Circle(A, C) → k_1
  32. OrthogonalLine(C, c) → i_1
  33. OrthogonalLine(A, c) → j_1
  34. Intersect(h_1, i_1, 1) → H
  35. Intersect(k_1, j_1, 1) → I
  36. Segment(I, H) → l_1
  37. Segment(H, C) → m_1
  38. Polygon(I, H, C, A) → poly3, i_2, h_2, c_2, a_3
  39. PointIn(poly3) → Pointpoly3_1
  40. PointIn(poly3) → Pointpoly3

AI Drawing Prompt Reference

Draw a right-angled triangle, label the hypotenuse and the two legs, and draw three squares on each side. Dynamically demonstrate that the area of the square on the hypotenuse equals the sum of the areas of the squares on the other two sides, using auxiliary lines and circles to verify the Pythagorean theorem through coordinate geometry and trigonometry.
The prompt above was compiled from the original drawing commands and is for reference only.