Students are given three triangles - one acute, one obtuse and one right - and are asked to cut them out. They are then asked to fold in the vertices to a point marked on a side. The sum of the three angles will then appear straight, and students are thus led to conjecture that the sum of the angles of a triangle is 180°.
Students next construct an exterior angle for one of their triangles. After they cut out the two remotes and position them within that exterior angle, they are led to conjecture that an exterior angle equals the sum of its two remotes.
Students are then led through rigorous proofs of these propositions.