In mathematics, a plane can be defined as a two-dimensional flat surface that extends up to infinity.We can divide planes into two types:- parallel planes and intersecting planes.
In this article, we are going to learn about planes, types of planes, planes in geometry, plane figures and properties of planes.
Table of Contents
What is a Plane?
Definition 1 = Plane can be defined as a two-dimensional flat surface that can extend up to infinity.
Definition 2 = A plane is a two-dimensional surface that can consist of line, a point and a three-dimensional space.
A plane has no width. We can see its example in coordinate geometry as it has 2 planes x and y.
As you already know, lines and points are very important parts of a plane.
Line
A line can be defined as a one dimensional which has length but no width.
Point
Point is simply a location in a plane with no length, breath and width.
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Types of Planes
In mathematics, we can categorize planes into two types:-
- Parallel planes
- Intersecting planes
1. Parallel planes
Parallel planes can be defined as planes that can never intersect each other.
Let us understand with an example:-
Here, the two planes are parallel to each other as they can never cross or intersect.
For example = our home’s ceiling and floor.
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2. Intersecting Planes
Intersecting planes are not parallel to each other and intersect always through a line.
It will get more clear with an example:-
In intersecting planes, two planes cannot intersect more than one line.
For example = connecting walls of a room
Planes in Algebra
In the Algebra , When the points are plotted in a geometrical plane, the position of any given point on the plane is resolved using the coordinates. Coordinates emphasize the correct location of the points on the plane.
The plane extends infinitely towards the x-axis and the y-axis on the number line. The number line is two-dimensional, where the plane extends endlessly. The plane has zero thickness, infinite width, and infinite length.
Properties of Plane
- When there are two distinct planes, they are either parallel to each other or intersecting planes.
- A line is either parallel to a plane, intersects the plane at a single point, or exists in the plane.
- When there are two different lines, which are perpendicular to the same plane, then they must be parallel to each other.
- When two different planes are perpendicular to the same line, they should be parallel to each other.
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Plane Figure
A plane figure can be defined as a geometric figure which has no thickness. It simply lies in one plane.
A plane figure is made up of two elements:-
- Line segments
- Curves
Examples of plane figures = Circle, Rectangle, Triangle, Square and so on. All the 2-d figures come under plane figures.
In the next article, we will learn about angle between the planes and equation of a plane.
