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Points, Lines, & Planes

Overview

The building blocks of reality.

What is it?

The three undefined terms upon which all of Euclidean geometry is built.

History

Euclid defined a point as 'that which has no part'—a concept of pure location without size.

Key Idea

Lines have arrows (forever). Segments have endpoints (stop).

Practice This Topic

Concept Guide

Plain English: Geometry is a game played on an imaginary board. A Point is a specific spot. A Line is a straight path that never ends. A Plane is a flat surface (like a wall) that goes on forever.

Real-world example: Game Design. A 'Vertex' is a point. An 'Edge' is a segment. A 'Face' is a plane.

How to do it

  1. Draw a dot and label it with a Capital Letter (Point A).
  2. Connect two points to make a Segment.
  3. Extend past the points with arrows to make a Line.
  4. Extend one side only to make a Ray.

Common Pitfall

Confusing Ray and Line. A Ray starts at a point and goes one way (like a laser). A Line goes forever in BOTH ways.

Word Problem
"You have three points: A, B, and C on a straight line. The distance A to B is 5. B to C is 3. What is A to C?"
Reasoning: Add the segments. 5 + 3 = 8. (Segment Addition Postulate).

Practice Examples

Notation
Line: <--> Ray: o--> Seg: o--o
Arrows matter.