Definition:Right Angle/Perpendicular

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Definition

In the words of Euclid:

When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.

(The Elements: Book $\text{I}$: Definition $10$)


Perpendicular.png

In the above diagram, the line $CD$ has been constructed so as to be a perpendicular to the line $AB$.


Foot of Perpendicular

The foot of a perpendicular is the point where it intersects the line to which it is at right angles.

In the above diagram, the point $C$ is the foot of the perpendicular $CD$.


Line Perpendicular to Plane

In the words of Euclid:

A straight line is at right angles to a plane when it makes right angles with all the straight lines which meet it and are in the plane.

(The Elements: Book $\text{XI}$: Definition $3$)


PerpendicularToPlane.png

In the above diagram, the line $AB$ has been constructed so as to be a perpendicular to the plane containing the straight lines $CD$ and $EF$.


Plane Perpendicular to Plane

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 $4$)


PlanePerpendicularToPlane.png

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.