Chapter 20: Synthetic geometry, constructions and proof
The axioms, theorems and corollaries of the shared geometry course, the constructions that go with them, and what a proof is.
The chapter problem
Why do the angles of a triangle add to 180°?. You have used this fact for years. You will prove it, from the axioms and the theorems that come before it, and by the end of the chapter you can say what a proof is and what it is not.
Where it is used: Construction, design, and the reasoning behind every geometrical fact you use.
Your turn to connect it: Which geometrical fact do you use most often without being able to say why it is true?
Sections
- 20.1 Axioms, theorems, corollaries and converses — tier O · refs GT.3
- 20.2 The constructions — tier O · refs GT.3
- 20.3 Angles and parallel lines — tier O · refs GT.3
- 20.4 Congruent triangles — tier O · refs GT.3
- 20.5 The isosceles triangle and its converse — tier O · refs GT.3
- 20.6 Parallelograms and their corollaries — tier O · refs GT.3
- 20.7 Similar triangles and proportionality — tier O · refs GT.3
- 20.8 The theorem of Pythagoras as a theorem — tier O · refs GT.3
- 20.9 Circles and their theorems — tier H · refs GT.3
- 20.10 Constructing a proof — tier O · refs GT.3
- 20.11 Evaluating someone else's proof — tier O · refs GT.3