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Ratios in Right Triangles

Ratios in Right Triangles
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2019-05-25 22:43
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric construction and properties of ratios in right triangles, involving core math concepts like the Pythagorean theorem, trigonometric functions (sine, cosine, tangent), and proportional relationships. It uses GeoGebra commands and objects such as Segment, OrthogonalLine, Point, Polygon, Dilate, Angle, and LaTeX for precise visualization. Suitable for high school mathematics education to understand ratio theorems and their practical applications.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Segment(A, C) → c
  5. Segment(C, B) → d
  6. Polygon(A, C, B) → poly1, b_1, a_1, c_1
  7. Dilate(A, 0.23, D) → I
  8. Dilate(C, 0.23, D) → K
  9. Dilate(B, 0.23, D) → J
  10. Polygon(I, K, J) → poly1', b', a', c'
  11. Dilate(A, 0.68, E) → H
  12. Dilate(C, 0.68, E) → F
  13. Dilate(B, 0.68, E) → G
  14. Polygon(H, F, G) → poly1'_1, b'_1, a'_1, c'_1
  15. Segment(J, K) → e
  16. Angle(K, J, I) → α
  17. Angle(F, G, H) → β
  18. Angle(C, B, A) → γ
  19. LaTeX(f, true, true) → text3
  20. Angle(J, I, K) → δ
  21. Angle(G, H, F) → ε
  22. Angle(B, A, C) → ζ