Pythagoras Extended. A Geometric Approach to the Cosine Rule

The motivation for this article was the desire to make the cosine rule in some way geometrically “obvious”. What we have ended up with is a mixture of inductive and deductive approaches which we hope goes some way to illuminating the cosine rule, and to enhancing students' relational understanding of it. The germ of these ideas can be sown soon after students have met Pythagoras, with the question “O.K., suppose the triangle ABC is not rightangled: what can we say about a 2 , b 2 and c 2 now?”