Definition:Right Angle/Perpendicular/Plane to Plane

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