2.1

Half-line

The set of all points on a line on a given side of a given point on the line

Line Seperation Postulate

Every point divides any line through that point into three disjoint sets: the point and two half-lines

2.1

Ray

The union of a half line and it's origin

Extends infinitely in one direction from a point

2.2

Segment

The set consisting of two points and all the points in between

Plane Seperation Postulate

Every line divides any plane containing the line into three disjoint sets: the line and two half-planes

2.3

Half-Plane

A subset of a plane consisting of all points on a given side of a line in the plane

2.3

Edge of a half-plane

The line that separates that plane into two half-planes

2.3

Opposite half-planes

The two half-planes that are separated by a particular line of the plane

2.3

Angle

The union of two distinct rays with a common endpoint

2.3

Sides of an angle

The two rays that form the angle

2.3

Vertex of an angle

The common endpoint of the two rays

2.3

Interior of an angle

The intersection of the two half-planes ech determined by a side of the angle and containing the other side (except for the vertex)

2.3

Exterior of an angle

The compliment of the union of the angle and its interior

2.4

Triangle

The union of segments that connect three noncollinear points

2.4

Closed curve

A curve that begins and ends at the same point

2.4

Simple curve

A curve that does not intersect itself

(unless the starting and ending points coincide)

2.4

Simple closed curve

A simple curve that is also a closed curve

2.4

Circle

The set of all points that are a given distance from a given point in a given plane

2.4

Center of the circle

The given point in the plane

2.4

Radius of a circle

A segment that connects a point on the circle with the center

2.4

Chord of a circle

A segment having both endpoints on the circle

2.4

Diameter

A chord that passes through the center of the circle

2.4

Arc

A curve that is a subset of a circle

2.4

Interior of a circle

The set of all planar points whose distance from the center of the circle is less than the length of the radius

2.4

Exterior of a circle

The set of all planar points whose distance from the center is greater than the length of the radius

2.4

Region

The union of a simple closed curve and its interior

The curve is the boundary of the region

Jordan Curve Theorem

Any simple closed curve divides a plane into three disjoint sets: the curve itself, its interior, and its exterior

2.5

Convex

Any two of its points determine a segment contained in the set

2.5

Concave

A set that is not convex

2.5

Polygon

A simple closed curve that consist only of segments

2.5

Side of a polygon

One of the segments that define the polygon

2.5

Vertex of a polygon

An endpoint of a side of the polygon

2.5

Angle of a polygon

An angle with two properties: its vertex is a vertex of the polygon and each side of the angle contains a side of the polygon

2.5

Equilateral Polygon

A polygon in which all sides have the same length

2.5

Equilangular Polygon

A convex polygon in which all angles have the same degree measure

2.5

Regular Polygon

A polygon that is both equilateral and equilangular

2.5

Diagonal of a polygon

Any segment that connects two vertices but is not a side of the polygon

2.5

Interior of a convex polygon

The intersection of the interiors of its angles

2.5

Exterior of a convex polygon

The union of the exteriors of its angles

2.6

Surface

A connected set of points in space having only the thickness of a point

2.6

Sphere

A surface in space consisting of the set of all points at a given distance from a given point

2.6

Radius of a sphere

a segment that connects a point of the sphere with the center

2.6

Closed Surface

A surface with a finite size that divides other points in space into an interior and an exterior

2.6

Solid

The union of a closed surface and its interior

2.6

Cone

The union of a region and all segments that connect the boundary of the region with a specific  noncoplanar point

2.6

Cylinder

The union of two regions of the same size and shape in defferent parallel planes, and the set of all segments that join corresponding points on the boundaries of the regions

2.6

Prism

A cylinder with polygonal regions as bases

2.6

Pyramid

A cone with a polygonal region as its base

2.7

Polyhedron

A closed surface made up of polygonal regions

2.7

Face of a Polyhedron

One of the polygonal regions that form the surface of the polyhedron