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Discovering the Pythagorean Theorem by Michael Powers

Discovering the Pythagorean Theorem by Michael Powers
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2020-04-12 03:05
TriangleAngleGeometric Construction
This activity provides general information to allow students to discover the Pythagorean Theorem on their own. It uses geometric construction tools like segments, circles, and intersections to help students understand the relationship between the sides of a right triangle. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. Circle(A, B) → c
  5. Intersect(c, g) → C, D
  6. OrthogonalLine(D, g) → i
  7. Intersect(i, h) → E
  8. Segment(D, A) → j
  9. Segment(D, E) → k
  10. Segment(E, B) → l
  11. Angle(A, D, E) → α
  12. Angle(D, E, B) → β
  13. Angle(E, B, A) → γ
  14. Angle(B, A, D) → δ
  15. Ray(A, D) → m
  16. Point(m) → F
  17. Segment(D, F) → n
  18. OrthogonalLine(F, n) → p
  19. Circle(F, D) → d
  20. Intersect(d, p) → G, H
  21. OrthogonalLine(H, p) → q
  22. OrthogonalLine(D, n) → r
  23. Intersect(r, q) → I
  24. Segment(H, F) → s
  25. Segment(H, I) → t
  26. Segment(I, D) → a
  27. Angle(I, H, F) → ε
  28. Angle(H, F, D) → ζ
  29. Angle(F, D, I) → η
  30. Angle(D, I, H) → θ
  31. Segment(F, E) → b
  32. OrthogonalLine(F, b) → e
  33. OrthogonalLine(E, b) → f_1
  34. Circle(F, E) → c_1
  35. Circle(E, F) → d_1
  36. Intersect(c_1, e, 2) → J
  37. Intersect(d_1, f_1, 2) → K
  38. Segment(J, K) → g_1
  39. Segment(J, F) → h_1
  40. Segment(K, E) → i_1
  41. Polygon(D, E, B, A) → q1, d_2, e_1, b_1, a_1
  42. Polygon(F, D, I, H) → q2, f_2, d_3, i_2, h_2
  43. Polygon(E, F, J, K) → q3, e_2, f_3, j_1, k_1
  44. InteriorAngles(q3) → ι, κ, λ, μ
  45. PointIn(q2) → Pointq2
  46. PointIn(q3) → Pointq3
  47. PointIn(q1) → Pointq1
  48. PointIn(q2) → L
  49. PointIn(q1) → M
  50. PointIn(q3) → N

AI Drawing Prompt Reference

Draw a right triangle ABC with A and B as the right angles. Construct lines perpendicular to AB and BC at A and B, respectively, intersecting at C to form right triangle ABC. Then, construct right triangle DEF with D on AB, E on BC, and F on AC. Draw a ray from D on line m, intersecting at F. Next, construct right triangle EFG with E and F as right angles, and G and H as intersection points. Finally, construct right triangle EJK with E and J as right angles, and K as the foot of the perpendicular from F.
The prompt above was compiled from the original drawing commands and is for reference only.