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Isosceles Triangles and Parallelograms on a Triangle

Isosceles Triangles and Parallelograms on a Triangle
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2017-07-27 23:02
TrianglePolygonGeometric Construction
This example demonstrates the construction of isosceles triangles and parallelograms on a triangle. Key mathematical concepts include the properties of isosceles triangles and the definition of parallelograms. Using GeoGebra commands such as Segment, LineBisector, Point, etc., isosceles triangles and parallelograms are constructed. Suitable for students at junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Segment(B, C) → g
  2. LineBisector(g) → p
  3. Point(p) → F
  4. Segment(C, C + (t4 * (F - C))) → r
  5. Segment(A, B) → f
  6. Midpoint(f) → J
  7. Segment(C, A) → h
  8. LineBisector(h) → l
  9. Point(l) → E
  10. Line(E, r) → m_1
  11. Segment(C, C + (t3 * (E - C))) → n_2
  12. Line(F, n_2) → n_1
  13. Intersect(m_1, n_1) → I
  14. LineBisector(f) → i
  15. Point(i) → D
  16. Midpoint(h) → K
  17. Segment(B, B + (t4 * (F - B))) → q
  18. Line(D, q) → t
  19. Segment(B, B + (t2 * (D - B))) → j
  20. Line(F, j) → s
  21. Intersect(s, t) → G
  22. Segment(A, A + (t2 * (D - A))) → k
  23. Polygon(A, B, D) → poly1, d, a, b
  24. Polygon(A, E, C) → poly2, c, a_1, e
  25. Polygon(C, F, B) → poly3, b_1, c_1, f_1
  26. Segment(A, A + (t3 * (E - A))) → m
  27. Line(D, m) → i_1
  28. Line(E, k) → j_1
  29. Intersect(i_1, j_1) → H
  30. Midpoint(g) → L
  31. Segment(G, G + (t8 * (K - G))) → r_1
  32. Segment(I, I + (t8 * (J - I))) → s_1
  33. Intersect(r_1, s_1) → M
  34. Segment(D, D + (t5 * (G - D))) → h_1
  35. Segment(F, F + (t5 * (G - F))) → g_1
  36. Segment(F, F + (t6 * (I - F))) → p_1
  37. Segment(E, E + (t6 * (I - E))) → q_1
  38. Segment(D, D + (t7 * (H - D))) → l_1
  39. Segment(E, E + (t7 * (H - E))) → k_1
  40. Segment(H, H + (t8 * (L - H))) → t_1