Planes in Geometry

Overview

This lecture introduces the concept of planes in geometry, focusing on how to define a plane using points and lines.

Understanding Planes

• A plane is a flat surface in three-dimensional space that extends infinitely in every direction.
• Unlike a line or point, a plane has length and width but no thickness.

Defining a Plane

• A single point cannot define a unique plane since infinite planes can pass through any point.
• Two points define a line, but infinite planes can contain that line and pass through both points.
• Three points can only define a unique plane if they are not all on the same line (non-colinear points).
• If three points are colinear (on the same line), they still allow infinite planes to pass through them.

Non-Colinear Points and Planes

• Three non-colinear points specify one unique plane.
• Any plane can be named using any three non-colinear points that lie on it.
• Naming a plane using three colinear points does not uniquely define the plane because those points are on infinite planes through the line they form.

Key Terms & Definitions

• Plane — a flat, two-dimensional surface that extends infinitely in all directions within three-dimensional space.
• Colinear — points that all lie on the same straight line.
• Non-Colinear — points that do not all lie on the same straight line; necessary to define a unique plane.

Action Items / Next Steps

• Identify and label non-colinear points on a plane in practice problems.
• Review textbook diagrams showing planes defined by non-colinear points.