Geometry: Convex Sets, Separation, Angles, Points, Lines, and Planes

Comprehensive vocabulary flashcards covering convex sets, separation postulates, angle basics, and fundamental terms of points, lines, and planes.

Convex Set

A set $M$ where for any two points $A$ and $B$ in the set, the entire line segment $\overline{AB}$ also lies in the set.

Half-planes (or Sides)

The two regions of a plane separated by a line located inside that plane.

Edge

The line inside a plane that separates the plane into two half-planes.

Lie on Opposite Sides of a Line

The position of two points when they are located on different half-planes separated by a given line.

Plane Separation Postulate

Given a line and a plane containing it, the points of the plane that do not lie on the line form two sets such that each set is convex, and if $P$ is in one set and $Q$ is in the other, then $\overline{PQ}$ intersects the line.

Space Separation Postulate

The points of space that do not lie in a given plane form two sets such that each set is convex, and if $P$ is in one set and $Q$ is in the other, then $\overline{PQ}$ intersects the plane.

Half-spaces

The two regions of space created when space is separated by a given plane.

Interior of an Angle

The smaller space located in between the rays forming an angle.

Exterior of an Angle

The larger space located outside the rays forming an angle.

Vertex

The common point shared by two rays that form an angle.

Side of an Angle

Each ray that forms an angle.

Interior of a Triangle

The set of points that lie in the interior of each of the three angles of the triangle.

Point

A singular location.

Line

A series of points that go infinitely in either direction.

Line Segment

A series of points that truncate with endpoints.

Ray

A series of points that go infinitely in one direction and have an endpoint in the other.

Plane

A two-dimensional, flat surface that extends without end.

Opposite Rays

Two rays that share the same endpoint, extend in opposite directions infinitely, and consist of collinear points.

Collinear Points

Points that lie on the same line.

Coplanar Points

Points that lie in the same plane.