Geometry - (Points, Lines, Planes, Rays, Segments)

Plane

A flat surface that has no thickness, extends infinitely in all directions.

Point

A location - no size, represented by a dot.

Identify the collinear points.

A, F and B are the points on the same line in the given diagram.

A line in a plane.

All points of the line are the points of intersection of a line and a plane when the line is contained in the plane.

Parallel Lines

Coplanar lines that do not intersect. symbol for parallel ||

Line Intersection Postulate

If two lines intersect, then they intersect in exactly one point.

Plane Intersection Postulate

If two planes intersect, then they intersect in exactly one line.

Naming a Line

May be named using a lower case script letter identified in the diagram, such as "l"

use the two endpoints of the segment. Example segment AB

Name the line segment

Named by two points identified on the line. Example line AB

Name the line.

May be named using 3 noncollinear points identified in the plane. (The 3 points form a triangle.) Example: ABC

Name the plane

May also be named using a capital script letter referenced in the plane. Example R

Name the plane in another way.

use the endpoint and another point in the direction the ray extends. Example ray AB

Name the ray.

A line parallel to a plane.

No points of intersection

A line passing through a plane.

One point of intersection.

Parallel Planes

Planes that do not intersect

Coplanar Points

Points S, T and R are coplanar points Points S, T, R and Q are noncoplanar points. Q is not located in the plane with S, T and R.

Collinear Points

Points on the same line

Coplanar Points

Points/Lines on the same plane

Line

Series of points that extend in opposite directions without end.

Ray

The part of a line consisting of one endpoint and all the points of the line to one side of the endpoint.

Line Segment

The part of a line consisting of two endpoints and all points between them.

Plane Postulate

Through any three noncollinear points there is exactly one plane. (If points form a triangle they form a plane.)

Line Postulate

Through any two points there is exactly one line.

Opposite Rays

Two collinear rays with the same endpoint, always form a line.