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Similar Right Triangles Demo by Kirsten Erlandsen

Similar Right Triangles Demo by Kirsten Erlandsen
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2019-02-12 04:41
TriangleCircleGeometric Construction
This example demonstrates the properties and criteria of similar right triangles. It involves core concepts like similarity criteria for right triangles, trigonometric functions, and area relationships. Construction uses commands such as Segment, Midpoint, OrthogonalLine, Circle, Semicircle, Point, Intersect, Angle, Polygon, CircleSector, Dilate, Vector, Translate, Rotate, CircleArc. Suitable for high school geometry instruction and construction practice.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Midpoint(a) → C_1
  3. OrthogonalLine(C_1, a) → b
  4. Circle(C_1, A) → c
  5. Semicircle(A, B) → d
  6. Point(d) → C
  7. Segment(A, C) → e
  8. Segment(C, B) → f
  9. OrthogonalLine(C, a) → g
  10. Intersect(g, a) → E
  11. Segment(C, E) → h
  12. Angle(B, E, C) → α
  13. Angle(A, C, B) → β
  14. Polygon(A, E, C) → poly1, d_1, a_1, e_1
  15. Polygon(E, B, C) → poly2, d_2, e_2, b_1
  16. Circle(A, 1) → k
  17. Circle(C, 1) → p
  18. Circle(B, 1) → q
  19. Intersect(p, e_1, 1) → F
  20. Intersect(a_1, b_1) → G
  21. Intersect(a_1, b_1) → H
  22. Intersect(p, h, 1) → I
  23. Intersect(p, f, 1) → J
  24. Intersect(q, a, 1) → K
  25. Intersect(q, f, 1) → L
  26. Intersect(k, a, 1) → M
  27. Intersect(k, e, 1) → N
  28. CircleSector(A, M, N) → r
  29. Dilate(C, If[-2 < i < -1, -1 - i, 0], E) → D'
  30. Segment(C, D') → j
  31. CircleSector(C, I, J) → s
  32. CircleSector(B, L, K) → t
  33. CircleSector(C, F, I) → c_1
  34. Angle(C, E, A) → γ
  35. Dilate(A, If[-0.5 < i < 0.5, 0.5 - i, 1], C) → A'
  36. Vector(A, A') → u
  37. Translate(r, u) → r'
  38. Rotate(r', If[-0.5 < i < 0.5, (((-(i + 0.5)) * 90))°], A') → r''
  39. CircleArc(A, M, N) → f_1
  40. Dilate(B, If[0.5 < i < 1.5, 1.5 - i], C) → B'
  41. Vector(B, B') → v
  42. Translate(t, v) → t'
  43. Rotate(t', If[0.5 < i < 1.5, (((i - 0.5) * 90))°], B') → t''
  44. CircleArc(B, L, K) → g_1
  45. Polygon(A, B, C) → poly3, d_3, a_2, b_2