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30-60 Right Triangle Side Relations

30-60 Right Triangle Side Relations
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2015-09-16 16:45
TriangleCircleTrigonometryGeometric Construction
This example demonstrates the side length relationships in a 30-60 right triangle. Key math concepts include special triangle properties, trigonometry, and geometric construction. It uses commands like Point, Segment, Circle, Midpoint, Intersect, Polygon, Angle, PolyLine to illustrate and analyze the triangle and incircle. Suitable for middle school and above students learning about special triangles and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a]) → B_2
  2. Segment(A, B_2) → b
  3. Circle(A, B_2) → c
  4. Circle(B_2, A) → d
  5. Midpoint(b) → B
  6. Intersect(c, d) → C, E, ,
  7. Segment(C, A) → e
  8. Segment(C, B) → f
  9. Segment(C, B_2) → g
  10. Polygon(C, B, A) → poly1, a_1, d_1, c_1
  11. Polygon(C, B_2, B) → poly2, c_2, d_2, b_1
  12. Angle(C, B, A) → α
  13. Angle(B, A, C) → β
  14. Angle(A, C, B) → γ
  15. Midpoint(e) → F
  16. Midpoint(f) → G
  17. Segment(A, B) → h_1
  18. Midpoint(h_1) → H
  19. Midpoint(H, B) → I
  20. Midpoint(I, H) → J
  21. PolyLine(F, J, G) → i
  22. Point(i) → K
  23. Midpoint(F, J) → L
  24. Midpoint(J, G) → M
  25. Intersect(xAxis, yAxis) → O
  26. Point(Circle[O, h]) → P
  27. Segment(O, P) → l
  28. Circle(O, P) → p
  29. Circle(P, O) → q
  30. Intersect(p, q, 1) → Q
  31. Midpoint(l) → R
  32. Segment(O, Q) → m
  33. Segment(R, Q) → n
  34. Segment(O, R) → r
  35. Polygon(O, R, Q) → poly3, q_1, o, r_1
  36. Midpoint(m) → S
  37. Midpoint(l) → T
  38. Midpoint(n) → U
  39. Midpoint(O, R) → A_1
  40. Midpoint(A_1, R) → B_1
  41. Midpoint(B_1, A_1) → C_1
  42. PolyLine(U, C_1, S) → s
  43. Point(s) → D_1
  44. Midpoint(S, C_1) → E_1
  45. Midpoint(C_1, U) → V
  46. Polygon(Q, O, R) → poly4, r_2, q_2, o_1
  47. Angle(R, O, Q) → δ
  48. Angle(O, Q, R) → ε
  49. Angle(Q, R, O) → ζ