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Similar Triangles and Trigonometry by vitullo

Similar Triangles and Trigonometry by vitullo
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2012-07-06 23:47
TriangleAngleTrigonometryGeometric Construction
This example demonstrates the properties and criteria of similar triangles, along with the definitions and calculations of trigonometric ratios (sine, cosine, tangent). Key math concepts include similar triangles, trigonometric functions, angle measurement, and distance calculation. Constructed using GeoGebra commands like Segment, OrthogonalLine, Point, Polygon, Dilate, Angle, and Distance. Suitable for high school students to learn and understand the relationship between similar triangles and trigonometric functions, ideal for classroom instruction or self-exploration.

GeoGebra Commands & Parameters

  1. Segment(A, B) → z
  2. OrthogonalLine(B, z) → b_2
  3. Point(b_2) → C
  4. Polygon(A, B, C) → poly1, AB, BC, AC
  5. Dilate(A, ScaleFactor, D) → A'
  6. Dilate(B, ScaleFactor, D) → B'
  7. Dilate(C, ScaleFactor, D) → C'
  8. Polygon(A', B', C') → poly1', c', a', b'
  9. Angle(C, B, A) → α
  10. Angle(C', B', A') → β
  11. Distance(A', B') → distanceA'B'
  12. Distance(B', C') → distanceB'C'
  13. Distance(C', A') → distanceC'A'
  14. Angle(B, A, C) → γ
  15. Angle(B', A', C') → δ