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Isosceles Right Triangle (45-45-90)

Isosceles Right Triangle (45-45-90)
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2018-08-14 01:22
TriangleTrigonometryGeometric Construction
This applet dynamically demonstrates the properties of an isosceles right triangle (45-45-90 triangle), guiding students to explore its characteristics. Key math concepts include isosceles triangles, right triangles, symmetry, trigonometry, and geometric constructions. It utilizes GeoGebra commands like Circle, Segment, OrthogonalLine, Rotate, Angle, Ray, Intersect, Polygon, Line, Point, Dilate, CircleSector, Vector, and Translate. Suitable for high school mathematics education, focusing on geometric construction and property investigation.

GeoGebra Commands & Parameters

  1. Circle(B, C) → c
  2. Segment(B, C) → a
  3. OrthogonalLine(C, a) → b
  4. Rotate(C, 45°, B) → C'
  5. Angle(C, B, C') → α
  6. Ray(B, C') → d
  7. Intersect(b, d) → A
  8. Segment(A, C) → e
  9. Segment(B, A) → f
  10. Polygon(B, C, A) → poly1, a_1, b_1, c_1
  11. Line(B, C) → h
  12. Point(h) → D
  13. Point(h) → E
  14. Ray(C, E) → i
  15. Point(i) → F
  16. Ray(C, F) → j
  17. Dilate(B, If[0 < g ≤ 1, 1 - g, 0], C) → B'
  18. Segment(B, B') → k
  19. Dilate(C, If[1 < g ≤ 2, 2 - g, 0], A) → C'_1
  20. Segment(C, C'_1) → l
  21. Circle(C, (0.15 * a)) → p
  22. Intersect(p, j, 1) → G
  23. Intersect(p, e, 1) → H
  24. Intersect(p, a, 1) → I
  25. Circle(A, (0.15 * a)) → q
  26. Circle(B, (0.15 * a)) → r
  27. Intersect(q, e, 1) → J
  28. Intersect(q, f, 1) → K
  29. CircleSector(C, H, I) → s
  30. Dilate(A, If[2 < g ≤ 3, 3 - g, 0], B) → A'
  31. Segment(A, A') → m
  32. CircleSector(A, K, J) → t
  33. Rotate(s, If[3.5 < g ≤ 4.5, ((-(g - 3.5)) * π / 2), -1.5707963267948966], C) → s'
  34. Dilate(A, If[5.5 < g ≤ 6.5, 6.5 - g, 0], B) → A'_1
  35. Vector(A, A'_1) → u
  36. Translate(t, u) → t'
  37. Rotate(B, If[4.5 < g ≤ 5.5, ((-(g - 4.5)) * π / 2), -1.5707963267948966], C) → B'_1
  38. Rotate(B', If[4.5 < g ≤ 5.5, ((-(g - 4.5)) * π / 2), -1.5707963267948966], C) → B''
  39. Segment(B'_1, B'') → k'
  40. Rotate(t', If[6.5 < g ≤ 7.5, (((-(g - 6.5)) * 5) * π / 4), -3.92699], B) → t''
  41. Dilate(A, If[7.5 < g ≤ 8.5, 8.5 - g, 0], C) → A'_2
  42. Vector(A, A'_2) → v
  43. Translate(t, v) → t'_1
  44. Rotate(t'_1, If[8.5 < g ≤ 9.5, (((-(g - 8.5)) * 3) * π / 4), -2.356194490192345], C) → d_1
  45. Dilate(A, If[9.5 < g ≤ 10.5, 10.5 - g, 0], C) → A'_3
  46. Vector(A, A'_3) → w
  47. Translate(t, w) → t'_2
  48. Rotate(t'_2, If[10.5 < g ≤ 11.5, ((-(g - 10.5)) * π / 2), -1.5707963267948966], C) → e_1