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Intersection of Squares Demo

Intersection of Squares Demo
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2017-09-11 10:13
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties and intersection points of two overlapping squares. It involves core concepts like polygons, intersection, midpoints, line segments, and circles. Constructed using commands such as Point, Polygon, Midpoint, Circle, Intersect, Line, OrthogonalLine, and Segment. Suitable for high school mathematics education to explore polygon intersections, geometric transformations, and coordinate systems.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A_1
  2. Polygon(A_1, B_1, 4) → poly1, f, g, h, i, C_1, D_1
  3. Midpoint(A_1, C_1) → D
  4. Circle(D, 4) → c
  5. Point(c) → F
  6. Polygon(D, F, 4) → poly2, j, k, l, m, G, H
  7. Intersect(h, m) → I
  8. Intersect(g, j) → J
  9. Polygon(D, I, C_1, J) → poly3, e, i_1, c_1, j_1
  10. Line(D, C) → p
  11. Intersect(c, p) → P, Q
  12. Intersect(poly1, poly2) → E, B, Intersect[poly1, poly2]_1, Intersect[poly1, poly2]_2
  13. Line(A_1, D) → n
  14. Intersect(p, n) → K
  15. Polygon(E, C, B, K) → poly4, r, m_1, s, k_1
  16. Polygon(B, A_1, E, K) → poly5, s_1, a, r_1, k_2
  17. Polygon(D_1, B, K, E) → poly6, d, s_2, k_3, r_2
  18. OrthogonalLine(K, n) → q
  19. Line(D_1, A_1) → t
  20. OrthogonalLine(K, t) → b
  21. Intersect(b, poly1) → L, N
  22. Intersect(poly2, poly1) → O, T, Intersect[poly2, poly1]_1, Intersect[poly2, poly1]_2
  23. Polygon(K, N, O) → poly7, o, k_4, n_1
  24. Line(K, t) → f_1
  25. Intersect(f_1, poly1) → U, V
  26. Polygon(K, U, T) → poly8, t_1, k_5, u
  27. Polygon(K, V, E) → poly9, r_3, k_6, v
  28. Polygon(K, N, B) → poly10, s_3, k_7, n_2
  29. Polygon(K, V, E) → poly11, r_4, k_8, v_1
  30. Polygon(L, B, K) → poly12, k_9, l_1, s_4
  31. Polygon(E, K, U) → poly13, u_1, r_5, k_{10}
  32. Polygon(K, L, B) → poly14, s_5, k_{11}, l_2
  33. Segment(A, B) → g_1
  34. Segment(B, C) → h_1