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Pythagorean Theorem Proof #6

Pythagorean Theorem Proof #6
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2015-10-23 21:50
TriangleCoordinate GeometryGeometric Construction
In collections GCSE Higher Ch5 Angles & Trigonometry
This example demonstrates the proof of the Pythagorean Theorem. It involves core concepts of triangles and geometric construction. Using GeoGebra commands such as point, segment, polygon, circle, and intersection, a dynamic geometric model is constructed. Suitable for middle school and above students to learn geometric proofs and dynamic geometry.

GeoGebra Commands & Parameters

  1. Point(m) → B
  2. Point(m) → A
  3. Segment(A, B) → a
  4. Polygon(A, B, 4) → poly1, b, c, d, e, C, D
  5. Point(a) → E
  6. Circle(A, E) → f
  7. Segment(A, E) → g
  8. Circle(D, g) → h
  9. Intersect(h, e, 1) → F
  10. Polygon(F, E, 4) → poly2, i, j, k, l, G, H
  11. Segment(A, E) → n
  12. Intersect(d, e) → I
  13. Intersect(d, k) → J
  14. Intersect(c, d) → K
  15. Intersect(c, j) → L
  16. Segment(F, I) → p
  17. Segment(J, K) → q
  18. Segment(L, B) → r
  19. Segment(A, F) → s
  20. Segment(I, J) → t
  21. Segment(K, L) → a_1
  22. Segment(E, B) → b_1
  23. Segment(F, E) → c_1
  24. Segment(F, J) → d_1
  25. Segment(J, L) → e_1
  26. Segment(E, L) → f_1
  27. Angle(I, A, B) → α
  28. Intersect(c, d) → M
  29. Angle(A, I, M) → β
  30. Angle(I, M, B) → γ
  31. Angle(M, B, A) → δ
  32. Segment(J, E) → g_1
  33. Polygon(E, A, F) → poly3, f_2, e_2, a_2
  34. Polygon(F, J, I) → poly4, i_1, f_3, j_1
  35. Polygon(J, K, L) → poly5, l_1, j_2, k_1
  36. Polygon(L, B, E) → poly6, e_3, l_2, b_2
  37. Polygon(F, J, E) → poly7, e_4, f_4, j_3
  38. Polygon(E, L, J) → poly8, j_4, e_5, l_3

AI Drawing Prompt Reference

Draw a right triangle ABC with points A and B as the endpoints of the legs and point C as the endpoint of the hypotenuse. Construct a circle centered at A with radius AE, and another circle centered at D with radius DG, which intersect at point F. Connect points A, E, F, I, J, K, and L to form several triangles and quadrilaterals, illustrating the proof of the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.