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Pythagorean Theorem Demo by francisgale

Pythagorean Theorem Demo by francisgale
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2013-04-26 12:36
TriangleFunctionGeometric Construction
This example demonstrates the Pythagorean Theorem in right-angled triangles, showing how the square of the hypotenuse equals the sum of the squares of the other two sides. It involves core concepts like right triangles, side lengths, and the Pythagorean Theorem. The construction uses commands such as Segment, Semicircle, Point, Polygon, Angle, OrthogonalLine, Circle, Intersect, and Line from GeoGebra. It is suitable for middle school students and above to learn and apply the theorem.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_2
  2. Semicircle(A, B) → c_2
  3. Point(c_2) → C
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Angle(B, A, C) → α
  6. Angle(C, B, A) → β
  7. Angle(A, C, B) → γ
  8. OrthogonalLine(C, a) → d
  9. OrthogonalLine(B, a) → e
  10. Circle(C, B) → f
  11. Intersect(f, d, 1) → D
  12. Line(D, a) → g
  13. Intersect(e, g) → E
  14. Polygon(C, B, E, D) → poly2, c_1, b_1, e_1, d_1
  15. OrthogonalLine(C, b) → h
  16. OrthogonalLine(A, b) → i
  17. Circle(A, C) → k
  18. Intersect(k, i, 1) → F
  19. Line(F, b) → j
  20. Intersect(h, j) → G
  21. Polygon(A, F, G, C) → poly3, a_1, f_1, g_1, c_3
  22. OrthogonalLine(A, c) → l
  23. OrthogonalLine(B, c) → m
  24. Circle(B, A) → p
  25. Intersect(p, m, 1) → H
  26. Line(H, c) → n
  27. Intersect(l, n) → I
  28. Polygon(A, B, H, I) → poly4, a_3, b_2, h_1, i_1
  29. Point(poly2) → J
  30. Point(a_3) → K
  31. Point(c_3) → L
  32. Segment(C, E) → q
  33. Segment(D, B) → r
  34. Point(q) → M
  35. Segment(A, H) → s
  36. Segment(B, I) → t
  37. Point(s) → N
  38. Segment(G, A) → j_1
  39. Segment(F, C) → k_1
  40. Point(j_1) → O

AI Drawing Prompt Reference

Draw a right triangle with labeled legs and hypotenuse. Create a semicircle with the hypotenuse as the diameter. Mark points where the semicircle intersects lines drawn from the endpoints of the hypotenuse to the opposite vertices, forming smaller triangles. Draw circles with diameters equal to the legs, intersecting perpendicular lines from the triangle's vertices to the legs, creating new points. Connect these points to illustrate the relationship between the smaller triangles and the original triangle, demonstrating the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.