Chapter 15: Synthetic geometry: foundations
The axioms, the first theorems, angles, congruent triangles and parallels — the beginning of the shared geometry course every paper draws on.
The chapter problem
A proof you can build on. You will prove that the angles of a triangle add to 180°, using only what comes before it. Every later theorem in this course will rest on results like this one, and by the end of the chapter you can say exactly what it rests on.
Where it is used: Every geometrical fact in the course, and the reasoning behind it.
Your turn to connect it: Which geometrical fact do you rely on most without knowing why it is true?
Sections
- 15.1 Axioms and the rules of deduction — tier O · refs 2.1
- 15.2 The first theorems on angles — tier O · refs 2.1
- 15.3 Congruent triangles — tier O · refs 2.1
- 15.4 Parallel lines — tier O · refs 2.1
- 15.5 The isosceles triangle and its converse — tier O · refs 2.1
- 15.6 Perpendicular lines and right angles — tier O · refs 2.1
- 15.7 Constructions 1–6 — tier O · refs 2.1
- 15.8 Writing a formal proof — tier O · refs 2.1