# Definition:Right Angle/Perpendicular/Plane to Plane

< Definition:Right Angle | Perpendicular(Redirected from Definition:Perpendicular Planes)

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## Definition

In the words of Euclid:

*A***plane**is**at right angles to a plane**when the straight lines drawn, in one of the planes, at right angles to the common section of the planes are at right angles to the remaining plane.

(*The Elements*: Book $\text{XI}$: Definition $4$)

In the above diagram, the two planes have been constructed so as to make lines perpendicular to their common section perpendicular to each other.

Thus the two planes are perpendicular to each other.

## Also known as

The word **normal** is often used for **perpendicular**, particularly in the context of **vector analysis**.

Also, in the context of **linear algebra** and **analysis**, the word **orthogonal** is often encountered, which is a generalization of the concept of **perpendicularity**, but in a more abstract context than **geometry**

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**perpendicular planes**