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Special Right Triangles by Rasha Tarek

Special Right Triangles by Rasha Tarek
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2016-04-14 19:59
TriangleTrigonometryGeometric Construction
This example demonstrates the construction and properties of two types of special right triangles: 30°-60°-90° and 45°-45°-90°. It involves core mathematical concepts such as trigonometric functions, proportional relationships, and geometric constructions. The construction is achieved using commands like Segment, Rotate, Angle, Midpoint, Point, Line, and Intersect in GeoGebra. It is suitable for high school students to learn and understand the geometric properties and practical applications of special right triangles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Rotate(B, 90°, A) → B'
  3. Angle(B, A, B') → α
  4. Segment(B', A) → b
  5. Segment(B', B) → c
  6. Midpoint(a) → C
  7. Midpoint(b) → D
  8. Midpoint(c) → E
  9. Angle(A, B', B) → β
  10. Angle(B', B, A) → γ
  11. Point(b) → F
  12. Point(c) → G
  13. Segment(F, G) → d
  14. Midpoint(d) → H
  15. Point(c) → I
  16. Point(a) → J
  17. Segment(I, J) → e
  18. Midpoint(e) → K
  19. Segment(L, M) → f
  20. Rotate(M, 90°, L) → M'
  21. Angle(M, L, M') → δ
  22. Rotate(L, (-(30°)), M) → L'
  23. Angle(L', M, L) → ε
  24. Line(L, M') → g
  25. Line(M, L') → h
  26. Intersect(h, g) → N
  27. Segment(M, N) → i
  28. Segment(L, N) → j
  29. Angle(L, N, M) → ζ
  30. Point(j) → O
  31. Point(i) → Q
  32. Segment(O, Q) → k
  33. Midpoint(k) → P
  34. Point(i) → R
  35. Point(f) → S
  36. Segment(R, S) → l
  37. Midpoint(l) → T
  38. Midpoint(i) → U
  39. Midpoint(j) → V
  40. Midpoint(f) → W