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What is a plane in geometry?

  • Last Updated : 02 Dec, 2021

Geometry is about the observation of shapes, sizes, angles, and dimensions of two-dimensional shapes. These two dimensions of geometrical figures include length and width. The 2D geometries, it is categorized into three types are euclidean geometry, spherical geometry, and hyperbolic geometry. Geometry is the mathematical study of geometrical figures and their properties.

These days geometry is used for computing designs, blueprints, construction, visual and graphic designing, infrastructural development.

What is a plane in geometry?

A plane is a two-dimensional flat surface that extends up to infinity. among its dimensions, it includes the length and width of the structure. Whereas, the plane is not concerned with thickness or curvatures. Anyone side of a cube, a piece of paper, floor are some examples of plane surfaces.

Types of planes

It is hard to determine a plane surface in real life. Hence, anyone side of a geometrical figure like a cube, a cuboid is considered to be a plane. These planes of 3D shapes are categorized into two types parallel plane and intersecting plane.

  • Parallel Plane: The plane that never intersects each other is known as a parallel plane. These plane lies perpendicular to each other.
  • Intersecting plane: The planes that always intersect each other along a line and aren’t parallel to each other are intersecting planes.

 Properties of a plane

Different properties of a plane can be seen based on its position and its interaction with the other planes. Some of the basic properties are mentioned below,

  • If two different planes are present in a 3D figure then, either they are parallel to each other or intersecting each other.
  • If two different lines are perpendicular to the same plane, The planes are parallel to each other.
  • If two different planes are perpendicular to the same line then they are parallel.

Sample Problems

Question 1: What are the examples of a plane in geometry?

Answer:

Piece of paper, a wall of a room, any one side of a cube or cuboid are real-life examples of planes in geometry.

Question 2: Can planes intersect?

Answer:

Yes, the intersection of the planes takes place on a line. They cannot intersect at a single point because planes extend to infinity.

Question 3: How many points are required to name a plane?

Answer:

In three-dimensional space, a plane can be defined by three-point which lie in different lines.

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