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Isosceles Triangle Demonstration

Isosceles Triangle Demonstration
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2017-11-27 21:09
TriangleAngleGeometric Construction
This example demonstrates the properties and construction of isosceles triangles. It involves core concepts like the definition of isosceles triangles, congruent base angles, and the perpendicularity of the angle bisector to the base. The construction uses commands and objects such as Polygon, Point, Segment, Line, Angle, Midpoint, Ray, OrthogonalLine, Mirror, and Circle in GeoGebra. It is suitable for middle school and above students learning geometric constructions and properties exploration.

GeoGebra Commands & Parameters

  1. Polygon(C, A, B) → poly1, b, c, a_1
  2. Point(Circle[D, 8]) → E
  3. Segment(D, E) → f
  4. Point(Circle[D, 8]) → F
  5. Segment(D, F) → g
  6. Point(Circle[F, 8]) → G
  7. Segment(F, G) → h
  8. Line(D, E) → i
  9. Polygon(D, F, G) → poly2, g_1, d, f_1
  10. Polygon(D, F, E) → poly3, e, d_1, f_2
  11. Segment(D, E) → j
  12. Angle(D, E, F) → α
  13. Angle(E, F, D) → β
  14. Angle(E, G, F) → γ
  15. Angle(F, D, E) → δ
  16. Midpoint(H, I) → J
  17. Ray(H, J) → k
  18. OrthogonalLine(J, k) → l
  19. Point(l) → K
  20. Segment(K, H) → m
  21. Segment(K, I) → n
  22. Point(k) → L
  23. Angle(L, I, K) → ε
  24. Mirror(M, N) → M'
  25. Segment(M, M') → p
  26. OrthogonalLine(N, p) → q
  27. Point(q) → O
  28. Segment(M, O) → r
  29. Segment(M', O) → s
  30. Segment(M', M) → t
  31. Ray(M, O) → h_1
  32. Point(h_1) → P
  33. Angle(P, O, M') → ζ
  34. Circle(Q, R) → c_1
  35. Point(c_1) → S
  36. Point(c_1) → T
  37. Segment(S, Q) → i_1
  38. Segment(T, Q) → k_1
  39. Segment(T, S) → j_1
  40. Angle(T, Q, S) → η
  41. Angle(S, T, Q) → θ
  42. Angle(Q, S, T) → ι
  43. Point(c) → U
  44. Segment(U, C) → l_1
  45. Polygon(V, W, Z) → t1, z_1, v, w
  46. Angle(V, W, Z) → κ
  47. Angle(Z, V, W) → λ
  48. Angle(W, Z, V) → μ
  49. Angle(D, F, E) → ν
  50. Angle(E, D, F) → ξ
  51. Angle(F, E, D) → ο
  52. Angle(E, F, G) → ρ
  53. Angle(G, E, F) → σ
  54. Angle(F, G, E) → τ