What a definition may use
Can you say what a point is, without using another new word? Try the cards below.
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Step 1 of 5
- Point, line — agreed, not defined.
- Line segment uses point and line.
- Ray uses point and line.
- Angle uses two rays with a shared end.
- "Direction" — no definition yet. Refused.
The job a definition does
No. Every try uses a word that itself needs a meaning.
A definition names one thing and fits no other thing. "A ray is a part of a line. It starts at a point and goes on one way." That uses only point and line.
A definition must use words that are already defined. Otherwise it explains nothing.
Try to define point. "A point has no size." Then what is size? Every try uses another new word.
Words that stay undefined
So geometry agrees that some words stay undefined. Point and line are two of them. They are called undefined terms. Later words are defined using them.
Rule: A definition may use only words already defined. Point and line are agreed, not defined.