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Special Right Triangles by Katie Lampart

Special Right Triangles by Katie Lampart
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2016-03-18 11:13
TriangleAngleTrigonometryGeometric 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 angle relationships, side length ratios, similarity transformations, and integer scaling. The construction uses commands like Segment, Rotate, Angle, Ray, Dilate, and Polygon, with objects A, B, α, β, γ, etc. It is suitable for high school mathematics education to 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. Ray(A, B') → b
  5. Dilate(B', 1.7320508, A) → C
  6. Segment(C, A) → c
  7. Segment(C, B) → d
  8. Angle(A, C, B) → β
  9. Angle(C, B, A) → γ
  10. Rotate(E, 90°, D) → F
  11. Angle(E, D, F) → δ
  12. Segment(E, D) → f
  13. Segment(D, F) → g
  14. Segment(F, E) → h
  15. Angle(D, F, E) → ε
  16. Angle(F, E, D) → ζ
  17. Segment(C, A) → j
  18. Segment(A, B) → k
  19. Segment(B, C) → l
  20. Segment(D, E) → m
  21. Segment(E, F) → n
  22. Segment(F, D) → p
  23. Polygon(D, E, F) → poly1, f_1, d_1, e