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Proof: Sine Rule 3

Proof: Sine Rule 3
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2018-12-09 20:45
AngleTrigonometryGeometric Construction
In collections Proof of Sine Rule, Cosine Rule, Area of a Triangle
This example demonstrates the proof of the Sine Rule, involving core mathematical concepts such as the relationship between sides and angles in a triangle and the properties of the sine function. The construction highlights the use of GeoGebra commands and objects like Intersect (intersection), Point (point), Segment (segment), OrthogonalLine (perpendicular line), Angle (angle), and Polygon (polygon) to build geometric figures and measure angles and side lengths. Suitable for high school students learning trigonometric functions and geometric proofs.

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. OrthogonalLine(B, b) → f
  7. Intersect(f, b) → Y
  8. Segment(Y, B) → m
  9. Angle(B, Y, C) → α
  10. Polygon(C, Y, B) → t1, b_1, c_1, y_1