Chapter 2 of seven · Geometry & Algebra

Structure

Parallels, triangles, and equations that are consequences instead of rules.

1. Transversals; corresponding anglesA line crossing two parallel lines meets them at the same angle, and here is why.Lesson
2. Alternate angles are equalA transversal crossing two parallel lines makes a second matching pair, on opposite sides.Lesson
3. Co-interior angles sum to 180A transversal crossing two parallel lines makes a pair that is not equal, but always sums to a straight angle.Lesson
4. The converse: equal alternate angles make lines parallelTurning the last three lessons around — from parallel lines predicting angles, to matching angles guaranteeing parallel lines.Lesson
5. The angle sum of a triangle is 180The first big payoff of the parallel postulate — and the first lesson to spend the construction tool the last one just built.Lesson
6. The exterior angle theoremWhat happens to a triangle's angle sum when one side is extended past a vertex — and why the last lesson already proved it.Lesson
7. The angle sum of any polygonOne new idea — splitting a shape into triangles — applied to a theorem this course already has.Lesson
8. The triangle inequalityThe last lesson of Phase 2 — and the only one that needed nothing from inside it at all.Lesson