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Exploring Similar Right Triangles by Mallory Cumpstone

Exploring Similar Right Triangles by Mallory Cumpstone
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2018-01-25 09:14
TriangleAngleTrigonometry
This applet allows students to discover the similarity of right triangles when the altitude is drawn to the hypotenuse. Key mathematical concepts include similar triangles, geometric mean, and trigonometric functions. The construction involves commands such as Semicircle, Point, Segment, etc. Suitable for middle school and above students to learn about similar triangles.

GeoGebra Commands & Parameters

  1. Semicircle(A, B) → d
  2. Point(d) → C
  3. Segment(C, B) → f
  4. Segment(A, C) → e
  5. Segment(A, B) → a
  6. Min(a, f) → m
  7. Min(a, e) → l
  8. Min(l, m) → n
  9. Midpoint(a) → C_1
  10. OrthogonalLine(C_1, a) → b
  11. Circle(C_1, A) → c
  12. OrthogonalLine(C, a) → g
  13. Intersect(g, a) → E
  14. Segment(C, E) → h
  15. Angle(B, E, C) → α
  16. Angle(A, C, B) → β
  17. Polygon(A, E, C) → poly1, d_1, a_1, e_1
  18. Polygon(E, B, C) → poly2, d_2, e_2, b_1
  19. Circle(A, (0.2 * n)) → k
  20. Circle(C, (0.2 * n)) → p
  21. Circle(B, (0.2 * n)) → q
  22. Intersect(p, e_1, 1) → F
  23. Intersect(a_1, b_1) → G
  24. Intersect(a_1, b_1) → H
  25. Intersect(p, h, 1) → I
  26. Intersect(p, f, 1) → J
  27. Intersect(q, a, 1) → K
  28. Intersect(q, f, 1) → L
  29. Intersect(k, a, 1) → M
  30. Intersect(k, e, 1) → N
  31. CircleSector(A, M, N) → r
  32. Dilate(C, If[-2 < i < -1, -1 - i, 0], E) → D'
  33. Segment(C, D') → j
  34. CircleSector(B, L, K) → t
  35. Angle(C, E, A) → γ
  36. Dilate(A, If[-0.5 < i ≤ 0.5, 0.5 - i, 0], C) → A'
  37. Vector(A, A') → u
  38. Translate(r, u) → r'
  39. CircleArc(A, M, N) → f_1
  40. Dilate(B, If[1.5 < i ≤ 2.5, 2.5 - i, 0], C) → B'
  41. Vector(B, B') → v
  42. Translate(t, v) → t'
  43. CircleArc(B, L, K) → g_1
  44. Polygon(A, B, C) → poly3, d_3, a_2, b_2
  45. Rotate(r', If[0.5 < i ≤ 1.5, ((-(i - 0.5)) * π / 2), -1.5707963267948966], C) → r''
  46. Translate(t, v) → t'_1
  47. Rotate(t'_1, If[2.5 < i ≤ 3.5, (((i - 2.5) * 90))°, 90°], C) → s