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New Pythagorean Theorem for Non-Similar Triangles

New Pythagorean Theorem for Non-Similar Triangles
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2019-07-31 14:00
TriangleCircleGeometric Construction
This example demonstrates a novel form of the Pythagorean theorem applied to non-similar triangles, exploring geometric properties and transformations. Core math concepts include the extension of Pythagoras' theorem, characteristics of non-similar triangles, geometric transformations, and coordinate geometry. Construction highlights involve commands like Circle, Point, Line, Intersect, Segment, Rotate, Angle, Polygon, PointIn, and Perimeter from GeoGebra. Suitable for high school and advanced learners exploring geometric proofs and theorem extensions.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Point(c) → C
  3. Line(C, A) → f
  4. Intersect(c, f, 2) → D
  5. Point(c) → B
  6. Segment(B, C) → g
  7. Point(f) → E
  8. Rotate(E, 90°, C) → E'
  9. Point(f) → F
  10. Segment(B, D) → h
  11. Angle(D, B, C) → α
  12. Polygon(D, B, 4) → poly1, i, j, k, l, G, H
  13. Polygon(B, C, 4) → poly2, m, n, p, q, I, J
  14. Polygon(C, D, 4) → poly3, r, s, t, b, K, L
  15. Point(k) → M
  16. Point(p) → N
  17. Point(t) → O
  18. Segment(M, B) → d
  19. Segment(M, D) → e
  20. Segment(B, N) → f_1
  21. Segment(D, O) → h_1
  22. Segment(O, C) → i_1
  23. Polygon(M, B, D) → t1, d_1, m_1, b_1
  24. Polygon(B, N, C) → t2, c_1, b_2, n_1
  25. Polygon(D, C, O) → t3, o, d_2, c_2
  26. PointIn(t1) → Pointt1_1
  27. PointIn(t2) → Pointt2_1
  28. PointIn(t3) → Pointt3_1
  29. Perimeter(t1) → perimetert1
  30. PointIn(t1) → Pointt1
  31. Perimeter(t2) → perimetert2
  32. PointIn(t2) → Pointt2_2
  33. PointIn(t2) → Pointt2_3
  34. Perimeter(t3) → perimetert3
  35. PointIn(t3) → Pointt3
  36. Perimeter(t2) → u
  37. PointIn(t2) → Pointt2

AI Drawing Prompt Reference

Draw a non-similar triangle ABC with points A, B, and C on circle c, line f passing through points C and A, and the second intersection of line f with circle c being point D. Construct segment BC, rotate point E 90 degrees to get E', segment BD, and angle DBC as α. Then construct polygons DBCG, BCDG, and CDGB, mark key points M, N, and O, and connect BM, BD, BN, DO, and OC. Construct polygons MBDC, BNDC, and DCBO, mark key points, and calculate perimeters.
The prompt above was compiled from the original drawing commands and is for reference only.