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Similar Right Triangles by Zach Schaver

Similar Right Triangles by Zach Schaver
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2019-01-05 02:46
TriangleTrigonometryGeometric Construction
This example demonstrates the properties and criteria of similar right triangles. It involves core mathematical concepts such as triangle similarity criteria, right triangle characteristics, trigonometric relationships, and geometric transformations. The construction utilizes GeoGebra commands and objects like points, lines, orthogonal lines, intersections, segments, angles, polygons, dilation, vectors, translation, rotation, and reflection. It is suitable for high school mathematics teaching, providing an intuitive display of the application of similar triangles in geometric problems.

GeoGebra Commands & Parameters

  1. Point(h) → A
  2. Line(A, B) → f
  3. OrthogonalLine(B, f) → g
  4. Intersect(h, g) → C
  5. Segment(A, B) → i
  6. Segment(B, C) → j
  7. Segment(C, A) → k
  8. OrthogonalLine(B, k) → l
  9. Intersect(l, k) → D
  10. Segment(B, D) → m
  11. Angle(C, D, B) → α
  12. Angle(A, B, C) → β
  13. Polygon(D, A, B) → t1, b, d, a_1
  14. Dilate(D, If[0 ≤ a < 1, 1 - a, 0], E) → D'
  15. Vector(D, D') → u
  16. Translate(D, u) → D'_1
  17. Translate(A, u) → A'
  18. Translate(B, u) → B'
  19. Polygon(D'_1, A', B') → t1', b', d'_1, a'
  20. Rotate(D'_1, If[1 ≤ a < 2, ((1 - a) * π / 2), (3 * π / 2)], E) → D''
  21. Rotate(A', If[1 ≤ a < 2, ((1 - a) * π / 2), (3 * π / 2)], E) → A''
  22. Rotate(B', If[1 ≤ a < 2, ((1 - a) * π / 2), (3 * π / 2)], E) → B''
  23. Polygon(D'', A'', B'') → t1'', b'', f_1, a''
  24. Polygon(D, C, B) → t2, b_1, d_1, c
  25. Dilate(D, If[2 ≤ a < 3, 3 - a, 0], F) → F'
  26. Vector(D, F') → v
  27. Translate(D, v) → D'_2
  28. Translate(C, v) → C'
  29. Translate(B, v) → B'_1
  30. Polygon(D'_2, C', B'_1) → t2', b'_1, d'_2, c'
  31. Polygon(A, B, C) → t3, c_1, a_2, b_2
  32. Dilate(B, If[3 ≤ a < 4, 4 - a, 0], G) → G'
  33. Vector(B, G') → w
  34. Translate(A, w) → A'_1
  35. Translate(B, w) → B'_2
  36. Translate(C, w) → C'_1
  37. Polygon(A'_1, B'_2, C'_1) → t3', c'_1, a'_1, b'_2
  38. Line(B, h) → n
  39. Point(n) → H
  40. Angle(C, B, H) → γ
  41. Rotate(A'_1, If[4 ≤ a < 5, ((a - 4) * γ), γ], G) → I
  42. Rotate(B'_2, If[4 ≤ a < 5, ((a - 4) * γ), γ], G) → J
  43. Rotate(C'_1, If[4 ≤ a < 5, ((a - 4) * γ), γ], G) → K
  44. Polygon(I, J, K) → t3'', k_1, i_1, j_1
  45. Line(J, K) → p
  46. Mirror(I, p) → I'
  47. Mirror(J, p) → J'
  48. Mirror(K, p) → K'
  49. Polygon(I', J', K') → t3''', k', i', j'
  50. Angle(B', D'_1, A') → δ
  51. Angle(B'', D'', A'') → ε
  52. Angle(C', D'_2, B'_1) → ζ
  53. Angle(A'_1, G', C'_1) → η
  54. Angle(I, J, K) → θ
  55. Angle(K', J', I') → ι