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Rectangles on Triangle

Rectangles on Triangle
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2017-07-27 21:03
TriangleCoordinate GeometryProbability & StatisticsGeometric Construction
This example demonstrates the dynamic construction of rectangles within a triangle and the geometric relationships involved. It involves core math concepts like rectangles, probability, secant lines or secants, power functions, LCM and GCD, and quadrilaterals. The construction uses commands and objects such as Rectangle, Segment, OrthogonalLine, Polygon, LineBisector, Intersect, Angle, and If from GeoGebra. It is suitable for high school mathematics education, exploring geometric transformations and applications in probability and statistics.

GeoGebra Commands & Parameters

  1. Rectangle1(C, B) → D, E
  2. Rectangle1(A, C) → F, G
  3. Rectangle1(B, A) → H, I
  4. Segment(A, B) → f
  5. Segment(B, C) → g
  6. Segment(C, A) → h
  7. OrthogonalLine(C, g) → k
  8. Polygon(B, D, E, C) → poly1, b, d, e, c
  9. Polygon(C, F, G, A) → poly2, c_1, f_1, g_1, a
  10. Polygon(A, H, I, B) → poly3, a_1, h_1, i, b_1
  11. Segment(F, F + (t6 * (E - F))) → j
  12. LineBisector(j) → n_2
  13. Segment(H, H + (t5 * (G - H))) → l
  14. LineBisector(l) → p
  15. Segment(D, D + (t4 * (I - D))) → m
  16. LineBisector(m) → q
  17. Intersect(q, n_2) → J
  18. Intersect(n_2, j) → K
  19. Intersect(p, l) → L
  20. Intersect(m, q) → M
  21. Angle(F, K, J) → α
  22. Angle(H, L, J) → β
  23. Angle(D, M, J) → γ
  24. Segment(K, E) → r
  25. Segment(K, F) → s
  26. Segment(G, L) → k_1
  27. Segment(L, H) → l_1
  28. Segment(D, M) → m_1
  29. Segment(M, I) → n_1
  30. Segment(D, D + (t4 * (I - D))) → p_1
  31. 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))]]) → q_1
  32. 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))]]) → r_1
  33. 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))]]) → s_1
  34. Segment(K3, K3 + (t7 * (J - K3))) → t
  35. Segment(L3, L3 + (t7 * (J - L3))) → i_1
  36. Segment(M3, M3 + (t7 * (J - M3))) → j_1