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Perpendicular Bisectors Exercise

Perpendicular Bisectors Exercise
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2019-05-04 05:56
TriangleCircleGeometric Construction
This example demonstrates how to construct triangles and circles using perpendicular bisectors. The core math concepts involved include geometric constructions, triangle properties, and circle properties. Construction highlights utilize GeoGebra commands such as Segment, LineBisector, Circle, Intersect, Rotate, CircleArc; objects include M, N, f, C, g, c, D, E, E', E'_1, D', D'_1, E'_2, E'_3, D'_2, D'_3, d, e, h, k, F, G, i, S, A, p, j, B, H, H', B', H'_1, B'_1, H'_2, B'_2, H'_3, B'_3, q, r, s. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Segment(M, N) → f
  2. LineBisector(f) → g
  3. Circle(M, C) → c
  4. Intersect(c, g) → D, E
  5. Rotate(E, 15°, M) → E'
  6. Rotate(E, (-(15°)), M) → E'_1
  7. Rotate(D, 15°, M) → D'
  8. Rotate(D, (-(15°)), M) → D'_1
  9. Rotate(E, 15°, N) → E'_2
  10. Rotate(E, (-(15°)), N) → E'_3
  11. Rotate(D, 15°, N) → D'_2
  12. Rotate(D, (-(15°)), N) → D'_3
  13. CircleArc(M, E'_1, E') → d
  14. CircleArc(N, E'_3, E'_2) → e
  15. CircleArc(M, D'_1, D') → h
  16. CircleArc(N, D'_3, D'_2) → k
  17. Intersect(h, k, 1) → F
  18. Intersect(d, e, 1) → G
  19. Segment(F, G) → i
  20. Intersect(i, f) → S
  21. Circle(M, A) → p
  22. LineBisector(M, S) → j
  23. Intersect(p, j) → B, H
  24. Rotate(H, 15°, M) → H'
  25. Rotate(B, 15°, M) → B'
  26. Rotate(H, 15°, S) → H'_1
  27. Rotate(B, 15°, S) → B'_1
  28. Rotate(H, (-(15°)), M) → H'_2
  29. Rotate(B, (-(15°)), M) → B'_2
  30. Rotate(H, (-(15°)), S) → H'_3
  31. Rotate(B, (-(15°)), S) → B'_3
  32. CircleArc(M, B'_2, B') → q
  33. CircleArc(M, H'_2, H') → r
  34. CircleArc(S, H'_3, H'_1) → s
  35. CircleArc(S, B'_3, B'_1) → t
  36. Intersect(q, t, 1) → I
  37. Intersect(r, s, 1) → J
  38. Segment(I, J) → l
  39. Intersect(f, l) → K
  40. Circle(K, L) → c_1
  41. LineBisector(K, S) → m
  42. Intersect(c_1, m) → O, P_1
  43. Rotate(P_1, 15°, K) → P'
  44. Rotate(O, 15°, K) → O'
  45. Rotate(P_1, 15°, S) → P'_1
  46. Rotate(O, 15°, S) → O'_1
  47. Rotate(P_1, (-(15°)), K) → P'_2
  48. Rotate(O, (-(15°)), K) → O'_2
  49. Rotate(P_1, (-(15°)), S) → P'_3
  50. Rotate(O, (-(15°)), S) → O'_3
  51. CircleArc(K, O'_2, O') → d_1
  52. CircleArc(K, P'_2, P') → e_1
  53. CircleArc(S, P'_3, P'_1) → f_1
  54. CircleArc(S, O'_3, O'_1) → g_1
  55. Intersect(d_1, g_1, 1) → Q
  56. Intersect(e_1, f_1, 1) → R
  57. Segment(Q, R) → n
  58. Intersect(f, n) → P

AI Drawing Prompt Reference

Draw a triangle and its perpendicular bisectors, then create circles centered at the triangle's vertices. Find the intersections of these circles with the bisectors. Rotate these intersection points to generate new ones, connect some to form segments, and draw arcs using these segments. Finally, connect the intersection points of the arcs to complete the figure, demonstrating the properties of perpendicular bisectors and circles.
The prompt above was compiled from the original drawing commands and is for reference only.