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Angles of a Right Triangle

Angles of a Right Triangle
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2016-08-20 22:33
TriangleAngleGeometric Construction
This example demonstrates the immediate corollary of the Triangle-Angle-Sum-Theorem. Key mathematical concepts include the properties of right triangles and the relationships between angles. Using GeoGebra commands such as Segment, Line, Ray, Point, etc., dynamic exploration of the angles in a right triangle is possible. Suitable for middle school and above students to learn geometric construction and angle relationships.

GeoGebra Commands & Parameters

  1. Segment(A, B) → g_1
  2. Line(A, B) → f
  3. Ray(A, B) → g
  4. Point(g_1) → C
  5. OrthogonalLine(C, g) → h
  6. Point(h) → D
  7. Ray(C, D) → i
  8. Point(i) → E
  9. Polygon(A, C, E) → poly1, e, a, c
  10. Segment(A, C) → j
  11. Segment(C, E) → k
  12. Segment(E, A) → l
  13. Min({j, k, l}) → b
  14. Circle(A, (0.2 * b)) → d
  15. Circle(E, (0.2 * b)) → p
  16. Circle(C, (0.2 * b)) → q
  17. Intersect(e, j) → F
  18. Intersect(d, l) → G,
  19. Intersect(d, j) → H,
  20. Intersect(q, j) → I,
  21. Intersect(q, k) → J,
  22. Intersect(p, l) → K,
  23. Intersect(p, k, 1) → L
  24. CircleSector(A, H, G) → r
  25. CircleSector(E, K, L) → s
  26. CircleSector(C, J, I) → t
  27. Ray(C, B) → n
  28. Rotate(t, If[0 < m ≤ 1, ((-m) * π / 2), ((-π)) / 2], C) → t'
  29. Dilate(E, If[1 < m ≤ 2, 2 - m, 0], C) → E'
  30. Vector(E, E') → u
  31. Translate(s, u) → s'
  32. Line(E, n) → f_1
  33. Point(f_1) → M
  34. Angle(M, E, K) → α
  35. Rotate(s', If[2 < m ≤ 3, ((-(m - 2)) * (π / 2 + α)), (-(π / 2 + α))], C) → s''
  36. Midpoint(A, C) → N
  37. Dilate(A, If[3 < m ≤ 4, 4 - m, 0], N) → A'
  38. Vector(A, A') → v
  39. Translate(r, v) → r'_1
  40. Rotate(r'_1, If[4 < m ≤ 5, ((m - 4) * (π - α)), π - α], N) → c_1
  41. Dilate(N, If[5 < m ≤ 6, 6 - m, 0], C) → N'
  42. Vector(N, N') → w
  43. Translate(c_1, w) → d_1