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3 Isosceles Triangles with Common Vertex and Vertex Angle

3 Isosceles Triangles with Common Vertex and Vertex Angle
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2017-07-29 06:08
TriangleAngleTransformationGeometric ConstructionSlider Animation
This example demonstrates the geometric construction and properties of three isosceles triangles sharing a common vertex and vertex angle. Key math concepts include isosceles triangles, vertex angles, rotation, midpoints, intersection points, and geometric transformations. The construction utilizes GeoGebra commands such as Rotate, Ray, Point, Polygon, Line, Midpoint, Intersect, Angle, Segment, and If. It is suitable for high school mathematics education, exploring symmetry and transformation relationships in isosceles triangles.

GeoGebra Commands & Parameters

  1. Rotate(B, 120°, A) → B'
  2. Ray(A, B') → f
  3. Point(f) → C
  4. Rotate(B, α, A) → B'_1
  5. Polygon(B, A, B'_1) → poly1, b'_1, b, a
  6. Line(C, b) → h
  7. Rotate(C, 120°, A) → C'_1
  8. Ray(A, C'_1) → g
  9. Point(g) → D
  10. Rotate(D, α, A) → D'
  11. Polygon(A, D, D') → poly3, d', a_2, d
  12. Midpoint(a_2) → G
  13. Rotate(C, α, A) → C'
  14. Polygon(A, C, C') → poly2, c', a_1, c_1
  15. Line(B'_1, c') → i
  16. Intersect(h, i) → E
  17. Angle(B, A, B') → β
  18. Angle(B, A, B'_1) → γ
  19. Angle(C, A, C') → δ
  20. Angle(C, A, C'_1) → ε
  21. Midpoint(a_1) → F
  22. Midpoint(a) → H
  23. Line(D, c_1) → j
  24. Line(C', d') → k
  25. Intersect(j, k) → I
  26. Line(D', b'_1) → l
  27. Line(B, d) → m
  28. Intersect(l, m) → J
  29. Segment(H, H + (t7 * (I - H))) → q
  30. Segment(G, G + (t7 * (E - G))) → p
  31. Intersect(p, q) → K
  32. Segment(F, F + (t7 * (J - F))) → n_1
  33. Segment(B, B + (t6 * (J - B))) → f_1
  34. Segment(D', D' + (t6 * (J - D'))) → e
  35. Segment(D, D + (t5 * (I - D))) → c
  36. Segment(C', C' + (t5 * (I - C'))) → t
  37. Segment(C, C + (t4 * (E - C))) → r
  38. Segment(B'_1, B'_1 + (t4 * (E - B'_1))) → s
  39. If(t2 ≤ 1, Segment[A, A + (t2 * (C - A))], If[t2 ≤ 2, Segment[C, C + ((t2 - 1) * (C' - C))], Segment[C', C' + ((t2 - 2) * (A - C'))]]) → g_1
  40. If(t1 ≤ 1, Segment[A, A + (t1 * (B - A))], If[t1 ≤ 2, Segment[B, B + ((t1 - 1) * (B'_1 - B))], Segment[B'_1, B'_1 + ((t1 - 2) * (A - B'_1))]]) → h_1
  41. If(t3 ≤ 1, Segment[A, A + (t3 * (D - A))], If[t3 ≤ 2, Segment[D, D + ((t3 - 1) * (D' - D))], Segment[D', D' + ((t3 - 2) * (A - D'))]]) → i_1