Plane Definition in Geometry: Everything You Need to Know
In geometry, a plane is a two-dimensional surface that contains all points that are the same distance from a given line. This line is called the plane's axis of symmetry. A plane does not have to be straight; it can be curved. The most familiar example of a curved plane is the surface of a sphere.
The word "plane" can also refer to the imaginary flat surface upon which a figure or object appears to rest. For example, a cube can be said to lie in or on a plane. This usage of the word "plane" is not, strictly speaking, correct since a cube has three dimensions and therefore cannot lie on a two-dimensional surface. However, it is common usage and you will often hear people say things like "the data lies in a plane." Just be aware that this usage is not technically correct.
When we talk about planes in geometry, we are usually referring to geometric planes. These are flat surfaces that extend infinitely in all directions. They are two-dimensional surfaces that do not have any thickness.
There are three types of geometric planes:
Parallel planes are planes that never intersect, no matter how far they are extended.
Perpendicular planes are planes that intersect at right angles.
Skew planes are planes that intersect at angles other than right angles.
It's important to note that the word "skew" does not necessarily imply that the lines are crooked or bent; it just means that they are not perpendicular or parallel.
In conclusion, a plane is a two-dimensional surface that contains all points that are the same distance from a given line (the plane's axis of symmetry). Planes can be straight or curved, and they can either be parallel, perpendicular, or skew. When we talk about planes in geometry, we are usually referring to geometric planes; these are flat surfaces that extend infinitely in all directions and do not have any thickness. Now you know everything there is to know about the definition of a plane in geometry!
FAQ
How do you define plane in geometry?
A plane is a two-dimensional surface that contains all points that are the same distance from a fixed line. The fixed line is called the plane's axis. Planes are named according to the number of axes they contain. For example, a plane that contains one axis is called a "one-dimensional plane." A plane that contains two axes is called a "two-dimensional plane." A plane that contains three axes is called a "three-dimensional plane."
What is a plane defined by?
A plane is defined by a point and a vector. The point is called the plane's origin, and the vector is called the plane's normal. The normal is perpendicular to the plane.
Why do 3 points define a plane?
Three points define a plane because they are all the same distance from the plane's axis. This means that the plane is flat.
What is the angle between two planes?
The angle between two planes is the angle between their normals.
What is the importance of plane in geometry?
Planes are important in geometry because they help define the three-dimensional space around us. Without planes, we would not be able to understand the world around us.