Let’s explore the Definition of a Plane in Geometry!

Definition of plane in geometry is simplified, along with easy explanation, different types of planes, real-life examples, etc.

Let’s explore the plane in geometry!

Let’s learn the basics, definition, meaning of plane in geometry.

Plane means a tiny word in geometry which means nothing but a surface not having any width or thickness.

- Planes are always two-dimensional.
- The plane can be extended any infinitely far.
- The plane has points or lines.
- It is basically a position, without any thickness.

The plane generally can be represented by

- ‘’Plane P’’, or
- ‘’Plane ABC’’ or
- ‘’Plane BCD’’ or
- ‘Plane ACD’ or
- ‘Plane ABCD’, etc.

Remember, this ‘A’, ‘B’, ‘C’ or ‘D’ can be written as small letters in many cases.

We can understand planes with few examples, like walls in our room or our books or tables.

- Take your physics book (Plane A), and just keep it on the table.
- Now the book is closed and it is a plane.
- Take another book (Plane B) and hold above the first book (Plane A)
- The height is equal at all the corners.

Take your physics book, and just keep it on the table. Now the book is closed and you touch its surface. This is nothing but a part of the plane. If you imagine that this surface is not limited to the book itself, just increase the surface far, you will get a plane.

You can do the same with the wall. Just extend the wall and you will see the plane!

If you imagine that this surface is not limited to the book itself, just increase the surface far, you will get a plane.

You can do the same with the wall. Just extend the wall and you will see the plane!

A plane in geometry is defined as a two-dimensional flat surface that can be extended infinitely far.

- The plane is sometimes called a two-dimensional surface.
- A plane consists of zero thickness, zero curvature but infinite width and length.

A plane is the analogue of three main things,

- Point
- Line
- 3-dimensional space

In the definition of the plane in geometry, we have extended the plane infinitely but what about the plane in algebra? Is it the same thing or different?

Let’s check!

We need to do a lot of calculations, and we use the coordinate plane to plot the points, lines as well as planes.

- Points are marked in two-dimensional areas, like (x, y)
- In this two-dimensional plot, there are two axes, one is the x-axis and another is the y-axis. Normally, the x-axis denotes the horizontal axis and the y-axis denotes the vertical axis.
- With the help of points, the plane can be drawn easily.
- Remember, any plane in algebra may contain several lines.
- All lines in the plane have arrow marks to indicated it as extended endlessly.

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There are few properties of plane, few of them are stated below,

- If there are three non-collinear points, a plane will be formed.
- If two straight lines are parallel, both these lines can for a plane.
- If two lines intersect, then also a plane can be formed.
- If you draw a line, and simultaneously one point you draw which is not on that line, then this line and point can form a plane.
- Collinear points along with one single point which not in the same line as collinear points, will form a plane.
- If you draw a line, that will be parallel to a plane or it will intersect to the plane at a point.
- If you take two or three different lines, and all are perpendicular to a plane, then these lines should be parallel.
- If two different planes, perpendicular to a line, then both the planes should be parallel.

In the geometry, we need to use a segment of planes, so we use ‘’plane figure’’ instead of plane and it can be various shapes, like

- Round shape
- Square
- Triangle
- Rectangle
- Pentagon
- Trapezoid etc.

Planes are categorized into two subcategories, as follows,

- Parallel Plane
- Intersecting plane

**Definition of parallel planes**

- As the name suggests, parallel planes mean if two or more planes are parallel.
- Parallel planes never intersect each other.

**Example of Parallel planes**

- Take two books and keep one book is one the table and another at some height. Make sure, the height between these two books is the same at all corners.
- What do you see from this example? It is simple! Both the book is parallel. Now, if you, think about the plane of both the books, that plane also will be parallel.

**Diagram & Explanation**

Parallel planes can be visualized with a simple example,

- Take your physics book (Plane A), and just keep it on the table.
- Now the book is closed and it is a plane.
- Take another book (Plane B) and hold above the first book (Plane A)
- The height is equal at all the corners.

Now you see both Plane A and Plane B are not intersecting, these are basically parallel.

**What is intersecting plane?**

- As the name suggests, intersecting planes mean if two or more planes are intersecting.
- Intersecting planes intersect in one line.
- Remember, it will be only one line at which two planes will intersect.

**Example of intersecting planes**

- If you are sitting in a room, look at any wall. Now, look at the floor as well as the same wall.
- Wall is a plane and a floor is also a plane.
- These two planes are intersected at a single line. This is nothing but an example of intersecting planes.
- If you imagine, the plane of the wall and plane of the floor is infinitely extended then also these two planes will be intersected in one line only.

**Diagram & Explanation**

Intersecting planes can be understood with the below example,

- In the above example, the wall (plane ‘A’) and the floor (Plane‘B’) intersect each other.
- A line ‘MN’ is created at the intersecting line.
- This ‘MN’ is a common line for both planes.

Refer to the below diagram and try to solve the small exercise.

Q1. From the diagram, what points are on the plane?

Q2. From the diagram, three points are not on the plane. What are these?

Q3. Form or list down the name of the plane from the diagram.

Q4. Name of the plan in a single letter.

Q1. It is clear from the diagram that Points Q, R, S, T, and U lie on the plane.

Q2. Points P, V, and W are not on the plane.

Q3. With the help of the diagram, this plane can be given the following names,

- QRS
- RST
- STU
- QRU
- QRT
- RSU
- QRST
- QRSTU etc.

Q4. In a single letter, this plane’s name is A as per the corner symbol.

Hence, we have learned the basic definition of plane in geometry is simplified, along with easy explanation, different types of planes, real-life examples, etc.

Any doubt, please write in the comment box.

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