Similar Right Triangles and Trig Ratios by E_Rushton

Similar Right Triangles and Trig Ratios by E_Rushton
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2016-11-05 16:53
This example demonstrates the properties of similar right triangles and their relationship with trigonometric ratios. Key math concepts include the criteria for triangle similarity, definitions of sine, cosine, and tangent functions, and the relationships between sides and angles in right triangles. Construction highlights involve GeoGebra commands such as Intersect, Circle, Point, Segment, OrthogonalLine, Tangent, Angle, and Polygon. It is suitable for high school students learning the geometric meaning of trigonometric functions and for analytical geometry instruction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A''
  2. Circle(A'', 1) → c
  3. Point(c) → B''
  4. Segment(A'', B'') → f
  5. OrthogonalLine(B'', xAxis) → g
  6. Intersect(g, xAxis) → C''
  7. Segment(A'', C'') → dx
  8. Segment(C'', B'') → dy
  9. OrthogonalLine(B'', yAxis) → j
  10. Intersect(j, yAxis) → D
  11. Segment(D, B'') → a
  12. Segment(D, A'') → b
  13. Tangent(B'', c) → h,
  14. Intersect(h, xAxis) → E
  15. Segment(B'', E) → t
  16. Segment(A'', E) → i
  17. Angle(B'', C'', A'') → α
  18. Angle(A'', B'', E) → β
  19. Polygon(A'', B'', C'') → poly1, c_1, a_1, b_1