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A Special Triangle & Its Properties (I)

A Special Triangle & Its Properties (I)
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2016-04-28 09:54
TriangleCircleGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Triangle Theorems
This example demonstrates the properties of an isosceles triangle, allowing students to discover the Isosceles Triangle Theorem and related theorems without angle measures. It involves core concepts like isosceles triangles, triangles, geometric mean, scatter plot, trapezoid, right triangles, and variance. Construction uses GeoGebra commands such as Circle, Intersect, Segment, Angle, Rotate, and Midpoint. Suitable for high school mathematics education to explore geometric theorems and properties.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Intersect(c, q) → O, P
  3. CircleArc(A, O, P) → d
  4. Point(d) → C
  5. CircleArc(A, C, P) → e
  6. Point(e) → D
  7. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
  8. Segment(A, A') → a
  9. Angle(C, A, D) → α
  10. Rotate(A, If[1 < j ≤ 2, ((j - 1) * α), α], A) → A'_1
  11. Rotate(A', If[1 < j ≤ 2, ((j - 1) * α), α], A) → A''
  12. Segment(A'_1, A'') → a'
  13. Segment(A, C) → b
  14. Segment(C, D) → f
  15. Segment(D, A) → g
  16. Midpoint(f) → E
  17. Segment(A, E) → h
  18. Midpoint(h) → F
  19. Segment(A, F) → i
  20. Segment(F, E) → k
  21. Circle(A, (0.35 * i)) → p
  22. Circle(E, (0.15 * Distance[D, E])) → r
  23. Intersect(r, f, 2) → G
  24. Intersect(r, h, 1) → H
  25. Intersect(r, f, 1) → I
  26. Intersect(p, b, 1) → J
  27. Intersect(p, h, 1) → K
  28. Intersect(p, g, 1) → L
  29. CircleSector(A, K, L) → s
  30. CircleSector(E, G, H) → t
  31. Circle(A, B) → c_1
  32. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], D) → C'
  33. Segment(C, C') → l
  34. Polygon(C, D, A) → poly1, a_1, c_2, d_1
  35. Circle(C, (0.2 * Distance[D, E])) → e_1
  36. Intersect(e_1, b) → M,
  37. Intersect(e_1, f) → N,
  38. CircleSector(C, N, M) → f_1
  39. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], F) → A'_2
  40. Segment(A, A'_2) → m
  41. Rotate(s, If[4 < j ≤ 5, ((-(j - 4)) * α / 2), ((-α)) / 2], A) → s'
  42. Dilate(F, If[5 < j ≤ 6, 6 - j, 0], E) → F'
  43. Segment(F, F') → n
  44. CircleArc(A, K, L) → g_1
  45. Dilate(E, If[6 < j ≤ 7, 7 - j, 0], D) → E'
  46. Segment(E, E') → b_1
  47. Rotate(E, If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E'_1
  48. Rotate(E', If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E''
  49. Segment(E'_1, E'') → h_1
  50. Rotate(t, If[8 < j ≤ 9, ((j - 8) * π / 2), 1.5707963267948966], E) → t'
  51. CircleArc(E, G, H) → k_1
  52. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], D) → C'_1
  53. Vector(C, C'_1) → u
  54. Translate(f_1, u) → p_1
  55. CircleArc(C, N, M) → q_1
  56. Angle(E, C, A) → β
  57. Rotate(p_1, If[10 < j ≤ 11, ((j - 10) * (π - β)), π - β], D) → r_1

AI Drawing Prompt Reference

Draw an isosceles triangle ABC with A and C as the base vertices and B as the apex. Use rotations and dilations to construct the triangle's medians, altitudes, angle bisectors, and form a complex shape with multiple arcs and segments.
The prompt above was compiled from the original drawing commands and is for reference only.