Geometric Proof of the Law of Cosines

This GeoGebra example provides an interactive geometric proof of the Law of Cosines for any triangle. It illustrates how the relationship between the sides and the cosine of an included angle arises from orthogonal projections and right-triangle decomposition. Key mathematical concepts include the Law of Cosines, triangle side-angle relationships, and Euclidean geometry principles. The construction uses fundamental GeoGebra commands: Line and OrthogonalLine to create auxiliary perpendiculars, Intersect to locate key points, Segment to draw triangle sides, and Angle to measure and display angles. Objects include vertices A, B, C; side segments a, b, c and their projections a', c'; multiple text labels (text1–text8); and interactive elements like button1. Designed for high school mathematics education, this resource supports conceptual understanding of trigonometric identities through visual reasoning and dynamic exploration.