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Proof of Sine Law by David Peterson

Proof of Sine Law by David Peterson
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2014-02-19 11:59
TriangleTrigonometryGeometric Construction
This example provides an interactive proof of the sine law, demonstrating the relationship between the sides and the sine of the opposite angles in a triangle. It uses commands such as Segment, OrthogonalLine, Polygon, Distance, and more. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. OrthogonalLine(C, a) → d
  5. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  6. Distance(A, C) → distanceAC
  7. Distance(B, C) → distanceBC
  8. Distance(A, B) → distanceAB
  9. Line(A, B) → e
  10. OrthogonalLine(C, e) → f
  11. Point(e) → D
  12. Intersect(f, e) → E
  13. Segment(C, E) → g
  14. Angle(D, E, C) → α
  15. Distance(E, C) → distanceEC

AI Drawing Prompt Reference

Draw a triangle with labeled sides. From one side, draw a perpendicular line to the opposite side, marking the intersection point. Connect the vertex to this point and measure the length of this segment and the angle formed. Display the relationship between the side lengths and the sines of the opposite angles to prove the sine law.
The prompt above was compiled from the original drawing commands and is for reference only.