Geometry is founded upon some very important basic concepts. These include points, angles, lines, and line segments. There are many postulates that govern the way that we can use these basic concepts. After the basic foundation is created, we can progress to harder, more advanced geometry.
Undefined Term: term that cannot be mathematically defined using other known words. The undefined terms point, line, and plane are the building blocks of geometry.
Point: Location that has no size (no dimension).
Line: Infinite series of points in a row (1-dimensional). It has direction and location and is always straight.
Plane: Any flat, 2-dimensional surface.
Undefined terms can be used to define other geometric terms:
Segment: Portion of a line that is ended by two points.
Ray: Portion of line that has only one endpoint and extends infinitely in the other direction.
Endpoint: Point at the end of a segment or at the start of a ray.
Space: Set of all points expanding in three dimensions. It has no shape and no limits.
Collinear: Points that lie on the same line.
Coplanar: Points or lines that lie within the same plane.
Intersection: Point or set of points where lines, planes, segments, or rays cross.
Postulate: Basic rule that is assumed to be true. Also known as an axiom.
Point
A capital label (A, L, F)
Line
A lowercase letter (line g) or two points on the line \(\overleftrightarrow{PQ} \text{or} \overleftrightarrow{QP}\)
Plane
A script capital letter (plane M) or three points not on a line (plane ABC)
Think of a plane as a huge sheet of paper!
Segment
The two endpoints (\(\overline{AB}\) or \(\overline{BA}\))
Ray
Endpoint and any other point on the ray (\(\overrightarrow{CD}\))
Everything in the figure below occupies 3-dimensional space.
When drawing or labeling geometric figures, be very specific!
Remember that arrows extend forever. In the figure below, even though the intersection is not shown, the two lines intersect at a point to the right.
There is exactly one line through any two points.
There is exactly one plane that contains any three non-collinear points.
A line connecting points in a plane also lies within the plane.
The intersection of any two distinct lines will be a single point.
The intersection of two distinct planes is a line