We may think of a point as a "dot" on a piece of paper or the pinpoint on a board. In geometry, we usually identify this point with a number or letter. A point has no length, width, or height - it just specifies an exact location. It is zero-dimensional.
Every point needs a name. To name a point, we can use a single capital letter. The following is a diagram of points A, B, and M:
We can use a line to connect two points on a sheet of paper. A line is one-dimensional. That is, a line has length, but no width or height. In geometry, a line is perfectly straight and extends forever in both directions. A line is uniquely determined by two points.
Lines need names just like points do, so that we can refer to them easily. To name a line, pick any two points on the line.
The line passing through the points A and B
is denoted by
A set of points that lie on the same line are said to be collinear.Pairs of lines can form intersecting lines, parallel lines, perpendicular lines and skew lines.
Because the length of any line is infinite, we sometimes use parts of a line. A line segment connects two endpoints. A line segment with two endpoints A and B is denoted by .
A line segment can also be drawn as part of a line.
The midpoint of a segment divides the segment into two segments of equal length. The diagram below shows the midpoint M of the line segment . Since M is the midpoint, we know that the lengths AM = MB.
A ray is part of a line that extends without end in one direction. It starts from one endpoint and extends forever in one direction.
A ray starting from point A and passing through B
is denoted by
Planes are two-dimensional. A plane has length and width, but no height, and extends infinitely on all sides. Planes are thought of as flat surfaces, like a tabletop. A plane is made up of an infinite amount of lines. Two-dimensional figures are called plane figures.
All the points and lines that lie on the same plane are said to be coplanar.
Space is the set of all points in the three dimensions - length, width and height. It is made up of an infinite number of planes. Figures in space are called solids.
Figures in space
This video explains and demonstrates the fundamental concepts (undefined terms) of geometry: points, lines, collinear, planes, and coplanar.
The following video gives the definitions of a point, a line, a plane, and space, as well as the symbols that are used in Geometry to represent each figure.
General Angle Basics: Angle Characteristics - rays, vertex,
Angle Classification - acute angle, right angle, obtuse angle, Complementary and Supplementary Angles
Understanding basic ideas in geometry and how we represent them with symbols