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Similar Right Triangles Demo by Philip Taylor

Similar Right Triangles Demo by Philip Taylor
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2019-02-11 11:55
TriangleAngleGeometric Construction
This example demonstrates the construction and properties of similar right triangles. It involves core math concepts like similarity criteria, right triangle characteristics, angle-side relationships, area calculations, and percentages. Construction uses commands such as Line, OrthogonalLine, Point, Polygon, Intersect, Segment, Angle, Rotate, Mirror, Vector, and Translate. Suitable for high school mathematics teaching on similarity and geometric transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. Point(g) → C
  4. Polygon(B, A, C) → t1, c, b, a
  5. OrthogonalLine(A, a) → h
  6. Intersect(h, a) → D
  7. Segment(A, D) → i
  8. Polygon(A, D, B) → t2, b_1, a_1, d
  9. Polygon(D, A, C) → t3, c_1, d_1, a_2
  10. Angle(C, D, A) → α
  11. Angle(D, B, A) → β
  12. Angle(A, D, B) → γ
  13. Angle(D, A, C) → δ
  14. Angle(A, C, D) → ε
  15. Angle(B, A, D) → ζ
  16. Rotate(D, ((-t) * (π - β)), A) → D'
  17. Rotate(A, ((-t) * (π - β)), A) → A'
  18. Rotate(C, ((-t) * (π - β)), A) → C'
  19. Polygon(D', A', C') → t3', c', d', a'
  20. Rotate(D, ((-t) * (π - β)), A) → D'_1
  21. Rotate(A, ((-t) * (π - β)), A) → A'_1
  22. Rotate(C, ((-t) * (π - β)), A) → C'_1
  23. Polygon(D'_1, A'_1, C'_1) → t3'_1, c'_1, d'_1, a'_1
  24. Rotate(A, (t * (π / 2 + β)), B) → A'_2
  25. Rotate(D, (t * (π / 2 + β)), B) → D'_2
  26. Rotate(B, (t * (π / 2 + β)), B) → B'
  27. Polygon(A'_2, D'_2, B') → t2', b', a'_2, d'_2
  28. Line(C, c) → j
  29. Mirror(B, j) → B'_1
  30. Mirror(A, j) → A'_3
  31. Mirror(C, j) → C'_2
  32. Rotate(B'_1, (t * π / 2), C) → E
  33. Rotate(A'_3, (t * π / 2), C) → F
  34. Rotate(C'_2, (t * π / 2), C) → G
  35. Polygon(E, F, G) → t1'', g_1, e, f_1
  36. Vector(D'_2 - F) → u
  37. Vector(D'_1 - F) → v
  38. Translate(A'_2, Vector[((-k) * u)]) → H
  39. Translate(D'_2, Vector[((-k) * u)]) → I
  40. Translate(B', Vector[((-k) * u)]) → B''
  41. Polygon(H, I, B'') → t2'', b'', h_1, i_1
  42. Translate(D', Vector[((-k) * v)]) → D''
  43. Translate(A', Vector[((-k) * v)]) → A''
  44. Translate(C', Vector[((-k) * v)]) → C''
  45. Polygon(D'', A'', C'') → t3'', c'', d'', a''
  46. Angle(C'', D'', A'') → θ
  47. Angle(G, F, E) → ι
  48. Angle(F, E, G) → κ
  49. Angle(D'', A'', C'') → λ
  50. Angle(I, B'', H) → μ
  51. Angle(B'', H, I) → ν
  52. Angle(A'', C'', D'') → ξ
  53. Angle(E, G, F) → ο