# What Does Normal Mean in Geometry?

A normal is a line that makes a $90$° angle with another line, meaning that it’s a line that makes a right angle with another line. This will almost always come up in a construction, so make sure you remember this.

## Perpendicular Bisector

A perpendicular bisector is a line that makes a $90$° angle in the exact middle of another line segment. In other words, the perpendicular bisector is a normal that splits a line segment into two equal parts. You construct a perpendicular bisector in the following way:

Rule

### InstructionsforConstructingthePerpendicularBisectorofaLine

1.
You have a line segment $l$ with two points $A$ and $B$.
2.
Put the point of your draft compass on $A$ and make two small arcs roughly above and below the midpoint between $A$ and $B$. In other words, one arc above the line $l$ and one arc below the line $l$.
3.
Without changing the distance between the legs of the draft compass, put the point of the draft compass on $B$ and do the same thing. Make sure the little arcs intersect to make two crosses—one above $l$ and one below $l$.
4.
Draw a straight line between the two crosses you just made with your draft compass.
5.
This line is the locus of points with equal distance to $A$ and $B$. The line makes a $90$° angle with $l$. We call this line the perpendicular bisector.

The only difference between the two normals—the perpendicular bisector and a normal from a point to a line—is the procedure for constructing them. Both yield the same result: Two lines forming a $90$° angle.

## Normal from the Point $P$ to a Line

Rule

### InstructionsforConstructingaNormalfromPointtoLine

1.
Draw the line $l$ and the point $P$ outside the line.
2.
Put the point of the draft compass on $P$ and make an arc that intersects the line $l$ in two places. Call the intersections $A$ and $B$.
3.
Move the point of the draft compass to $A$ and make an arc on the opposite side of $l$ to $P$.
4.
Do the same from $B$ without changing the distance between the two legs of the draft compass, and make sure the two arcs intersect.
5.
Draw a line from $P$ to the new intersection.
6.
You have now drawn the normal from point $P$ to the line.