AI Tutor
Imagine playing a board game where nobody agrees on the rules, what the game pieces are called, or how to win.
Geometry avoids that chaos by building a strict hierarchy: definitions, postulates, and theorems.
How do we make sure everyone means the exact same thing when naming a geometric object?

Definitions

A definition is an exact description of a mathematical term using words we already understand.
Definitions are always reversible—they work both forward and backward as an "if and only if" statement.
For example, a midpoint is defined as the point that divides a segment into two congruent segments.
What if a statement seems completely obvious, but we cannot actually prove it from simpler facts?

Postulates

A postulate (also called an axiom) is a basic rule accepted as true without proof.
Around 300 BCE, Greek mathematician Euclid realized you cannot prove everything without hitting an endless loop—so he established five starting rules as common ground.