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Cosine Rule Proof

Cosine Rule Proof
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2018-12-09 20:55
TriangleTrigonometryGeometric Construction
In collections Proof of Sine Rule, Cosine Rule, Area of a Triangle
This example demonstrates the application of the Cosine Rule in triangles, visually proving the relationship between side lengths and angles. Core math concepts include the Cosine Rule, triangle geometry, and angle measurement. Construction highlights involve GeoGebra commands/objects like Intersect, Point, Segment, Polygon, and Angle. Suitable for high school mathematics teaching or student exploration of 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. Segment(C, X) → h
  7. Polygon(C, A, X) → t1, x_1, c_1, a_1
  8. Angle(C, X, A) → α

AI Drawing Prompt Reference

Draw a triangle with labeled vertices and connect each pair of vertices to form three sides. Inside the triangle, draw a perpendicular line from one vertex to the opposite side, creating a height. Label the three angles and the lengths of the sides, visually demonstrating the proof of the cosine rule to show the relationship between side lengths and angles.
The prompt above was compiled from the original drawing commands and is for reference only.