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Ratios in Right Triangles by omirontchik (2)

Ratios in Right Triangles by omirontchik (2)
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2018-03-01 20:08
TriangleTrigonometryGeometric Construction
This example demonstrates the ratio relationships between side lengths and angles in right triangles. Key math concepts include the Pythagorean theorem, trigonometric functions (sine, cosine, tangent), and ratio relationships. Construction involves commands like Segment, OrthogonalLine, Point, Polygon, Dilate, Angle, LaTeX to build the right triangle and illustrate the ratios. Suitable for high school mathematics teaching, helping students understand geometric transformations and ratio applications in right triangles.

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