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Draw a straight line. What gives you the right to draw it?

Nothing says a line must be there when you want one. So geometry starts by agreeing on a few things. Everything else is built from them.

What this chapter covers

• Examples are not proof. Forty cases pass. The claim is still wrong.
• Definitions. A new word may use only words we already have.
• Axioms. Two agreements that all of maths uses.
• Postulates. Five agreements about points, lines and circles.
• Construction. Each step is allowed by a postulate.
• A square. Same area as a rectangle, built with care.
• Proof parts. The five layers under every proof.

Need a quick catch-up?

These earlier ideas help. Nothing here needs them perfectly.

• A claim that fails on one late case.
• Point, line and ray.
• Copying an angle. The line equally far from two points.
• The balance beam. Going back from a square to its side.

This is the chapter Introduction to Euclid's Geometry: Axioms and Postulates. Every proof you meet later uses it.