New Pythagorean Theorem - Complex Shapes

New Pythagorean Theorem - Complex Shapes
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2019-07-30 10:46
This example demonstrates the application of the new Pythagorean theorem in complex shapes. Key mathematical concepts include geometric transformations, similar triangles, and geometric mean. Using GeoGebra commands such as Circle, Point, Line, Intersect, etc., complex geometric shapes can be constructed. Suitable for high school mathematics education and learning.

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. Polygon(D, B, 3) → poly1, i, j, k, G
  12. Polygon(B, C, 3) → poly2, l, m, n, H
  13. Polygon(C, D, 3) → poly3, p, q, r, I
  14. Polygon(G, B, 4) → poly4, s, t, b, d, J, K
  15. Polygon(H, C, 4) → poly5, e, f_1, g_1, h_1, L, M
  16. Polygon(I, D, 4) → poly6, i_1, j_1, k_1, l_1, N, O
  17. Polygon(M, L, 3) → poly7, m_1, n_1, p_1, P
  18. Polygon(K, J, 3) → poly8, q_1, r_1, s_1, Q
  19. Polygon(O, N, 3) → poly9, t_1, a_1, b_1, R
  20. Polygon(Q, J, B, D, G, K) → poly10, q_2, j_2, b_2, d_1, g_2, k_2
  21. Polygon(B, H, M, P, L, C) → poly11, b_3, h_2, m_2, p_2, l_2, c_1
  22. Polygon(D, N, R, O, I, C) → poly12, d_2, n_2, r_2, o, ı, c_2
  23. PointIn(poly10) → Pointpoly10_1
  24. PointIn(poly11) → Pointpoly11_1
  25. PointIn(poly12) → Pointpoly12_1
  26. Perimeter(poly10) → perimeterpoly10
  27. PointIn(poly10) → Pointpoly10
  28. Perimeter(poly11) → perimeterpoly11
  29. PointIn(poly11) → Pointpoly11
  30. Perimeter(poly12) → perimeterpoly12
  31. PointIn(poly12) → Pointpoly12

AI Drawing Prompt Reference

Draw a complex geometric shape with multiple triangles and quadrilaterals. Start by drawing a circle, then take point C on the circle and draw a line f through C, intersecting the circle at points B and D. Rotate point E to get E', and draw line segment BG. Construct several triangles and quadrilaterals, such as triangle BCD and quadrilateral GBDH, and finally calculate and display the perimeter of each quadrilateral.
The prompt above was compiled from the original drawing commands and is for reference only.