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Proof: Sine Rule 1

Proof: Sine Rule 1
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2018-12-09 20:41
TriangleTrigonometryGeometric Construction
In collections Proof of Sine Rule, Cosine Rule, Area of a Triangle
This example demonstrates the application of the Sine Rule in any triangle, proving that the ratio of the lengths of the sides to the sines of their opposite angles is constant. It involves core mathematical concepts such as trigonometric functions, geometric constructions, similar triangles, and proportional relationships. The construction uses GeoGebra commands and objects like Intersect, Point, Segment, Polygon, and Angle to build the triangle, perpendiculars, and angle measurements. Suitable for high school students learning and understanding the proof of the Sine Rule, as well as geometric intuitive teaching.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Segment(C, A) → b
  4. Segment(A, B) → c
  5. Segment(B, C) → a
  6. Segment(C, X) → h
  7. Polygon(C, X, B) → t1, b_1, c_1, x_1
  8. Angle(C, X, A) → α

AI Drawing Prompt Reference

Draw an arbitrary triangle and label its three sides and angles. From each vertex, draw perpendiculars to the opposite sides, forming three right triangles. Measure the angles and corresponding side lengths, showing that the ratio of each side length to the sine of its opposite angle is constant, proving the Sine Rule.
The prompt above was compiled from the original drawing commands and is for reference only.