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.