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Squares and Parallelograms on Triangle by Doug Kuhlmann (2)

Squares and Parallelograms on Triangle by Doug Kuhlmann (2)
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2017-07-27 04:30
TrianglePolygonCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the construction of squares and parallelograms on a triangle. Key mathematical concepts include geometric construction, coordinate geometry, and solid geometry. Using GeoGebra commands such as Polygon, Segment, Line, and Intersect, the properties and relationships of these geometric shapes are visually illustrated. Suitable for middle school and above students and teachers.

GeoGebra Commands & Parameters

  1. Polygon(B, A, 4) → poly3, r, s, t, a, H, I
  2. Segment(A, B) → f
  3. Segment(B, C) → g
  4. Segment(C, A) → h
  5. Polygon(C, B, 4) → poly1, i, j, k, l, D, E
  6. Polygon(A, C, 4) → poly2, m, n_1, p, q, F, G
  7. If(t1 ≤ 1, Segment[B, B + (t1 * (D - B))], If[t1 ≤ 2, Segment[D, D + ((t1 - 1) * (E - D))], Segment[E, E + ((t1 - 2) * (C - E))]]) → e
  8. If(t1 ≤ 1, Segment[B, B + (t1 * (D - B))], If[t1 ≤ 2, Segment[D, D + ((t1 - 1) * (E - D))], Segment[E, E + ((t1 - 2) * (C - E))]]) → f_1
  9. If(t2 ≤ 1, Segment[C, C + (t2 * (F - C))], If[t2 ≤ 2, Segment[F, F + ((t2 - 1) * (G - F))], Segment[G, G + ((t2 - 2) * (A - G))]]) → i_1
  10. If(t3 ≤ 1, Segment[A, A + (t3 * (H - A))], If[t3 ≤ 2, Segment[H, H + ((t3 - 1) * (I - H))], Segment[I, I + ((t3 - 2) * (B - I))]]) → g_1
  11. Line(E, n_1) → b
  12. Line(F, e) → c
  13. Intersect(b, c) → J
  14. Line(H, i_1) → d
  15. Line(G, s) → h_1
  16. Intersect(d, h_1) → K
  17. Line(I, j) → j_1
  18. Line(D, g_1) → k_1
  19. Intersect(k_1, j_1) → L
  20. Segment(E, E + (t4 * (J - E))) → l_1
  21. Segment(F, F + (t4 * (J - F))) → m_1
  22. Segment(G, G + (t5 * (K - G))) → p_1
  23. Segment(H, H + (t5 * (K - H))) → q_1
  24. Segment(I, I + (t6 * (L - I))) → r_1
  25. Segment(D, D + (t6 * (L - D))) → s_1
  26. Ray(L, B) → t_1
  27. Ray(K, A) → a_1
  28. Midpoint(J, C) → N
  29. Midpoint(K, A) → O
  30. Midpoint(L, B) → P
  31. Midpoint(F, A) → Q
  32. Midpoint(H, B) → R
  33. Midpoint(D, C) → S
  34. Segment(P, P + (t7 * (Q - P))) → d_1
  35. Segment(N, N + (t7 * (R - N))) → c_1
  36. Segment(O, O + (t7 * (S - O))) → b_1
  37. Intersect(d_1, c_1) → M