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Special Right Triangles by Amy Fligor

Special Right Triangles by Amy Fligor
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2017-04-02 08:18
TriangleTrigonometryCoordinate Geometry
This example demonstrates the properties of special right triangles. Key mathematical concepts include right triangles, trigonometry, and rotation. Using GeoGebra commands such as Semicircle, Segment, Midpoint, and Rotate, the construction process of right triangles is dynamically shown. Suitable for middle and high school students learning geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Semicircle(K, B_1) → c
  2. Segment(K, B_1) → f
  3. Midpoint(K, B_1) → C
  4. Rotate(B_1, 45°, C) → A
  5. Angle(B_1, C, A) → α
  6. Rotate(B_1, 90°, C) → B'_1
  7. Angle(B_1, C, B'_1) → β
  8. Rotate(B_1, 150°, C) → D
  9. Segment(C, A) → g
  10. Segment(C, D) → h
  11. OrthogonalLine(D, f) → i
  12. OrthogonalLine(A, f) → j
  13. OrthogonalLine(B'_1, f) → k
  14. Intersect(i, f) → E
  15. Intersect(j, f) → B
  16. Segment(D, E) → l
  17. Segment(B'_1, C) → m
  18. Segment(A, B) → n
  19. Angle(D, C, E) → γ
  20. Angle(C, E, D) → δ
  21. Angle(A, B, C) → ε
  22. Distance(C, A) → distanceCB'
  23. Midpoint(C, A) →
  24. Distance(A, B) → distanceB'E
  25. Midpoint(A, B) →
  26. Distance(B, C) → distanceEC
  27. Midpoint(B, C) →
  28. Distance(C, E) → distanceCD
  29. Midpoint(C, E) →
  30. Distance(E, D) → distanceDB'2
  31. Midpoint(E, D) →
  32. Distance(D, C) → distanceB'2C
  33. Midpoint(D, C) →