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Points, Lines, & Planes

The Hook

The building blocks of reality.

What is it?

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

Time Travel (History)

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

Cheat Code

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

Practice This Now!

The Field Guide

In 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.

In The Real World: 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.

Booby Trap!

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

Real World Challenge
"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?"
The Logic: Add the segments. 5 + 3 = 8. (Segment Addition Postulate).

Training Drills

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