Key Concepts: Points, Lines, and Planes

Point

A Point is the most basic building block of geometry. It represents a location in space with no size, no width, no length, and no depth. Points are named with capital letters (e.g., Point A).

Line

A Line is a straight path that extends infinitely in both directions. It has no thickness and contains infinitely many points. A Line is named by any two points on it (e.g., Line AB, written ←→ AB) or by a lowercase letter.

• Collinear points: Points that lie on the same Line.
• Non-Collinear points: Points that do NOT lie on the same Line.

Plane

A Plane is a flat surface that extends infinitely in all directions. It has length and width but no thickness. A Plane is named by three Non-Collinear points (e.g., Plane ABC) or by a capital letter.

• Coplanar points: Points that lie in the same Plane.
• Non-Coplanar points: Points that do NOT all lie in the same Plane.

Key Postulates

• Through any two points, there is exactly one Line.
• Through any three Non-Collinear points, there is exactly one Plane.
• A Line contains at least two points.
• A Plane contains at least three Non-Collinear points.
• If two points lie in a Plane, the entire Line containing them lies in the Plane.
• If two planes intersect, their intersection is a Line.