 # Construct A Perpendicular Line

In these lessons, we will learn

• how to construct a perpendicular to a line, through a point on a line.
• how to construct a perpendicular to a line, through a point not on a line.
Related Topics: More Geometry Lessons

### Construct a perpendicular to a line, through a point on the line

We will now show how to construct a perpendicular to a line segment, through a point on the line.

Example :

Construct a line perpendicular to PQ through the point R on PQ. Solution:

Step 1: Stretch your compasses a short length. It can be any length. Put the sharp end of the compasses on point R and mark two arcs S and T on the line PQ. Step 2: Stretch the compasses a little more. Put the sharp end of the compasses on point S and make an arc with pencil end. Do the same on point T but make sure that the second arc intersects the first arc. Step3: Draw a line from point R to the point where the arcs intersect. This line is perpendicular to PQ and passes through the point R. How to construct a perpendicular to a line segment, through a point on the line?
1. Place compass point on the given point, and draw arc either side of point such that it intersects line twice.
2. Place compass on each arc-line intersection, and draw an arc above the line, without changing the compasses' width.
3. Using a straight edge, connect this intersection point to the original point with a straight line.
How to construct a perpendicular line from a point on a line?

### Construct a perpendicular to a line, through a point not on the line

We will now construct a perpendicular to a line, through a point not on the line.

Example :

Construct a line perpendicular to the line AB and passing through the point P, that is not on the line, Solution:

Step 1: Put the sharp end of your compasses on point P, stretch the compasses and mark two arcs R and S on the line AB. Step2: Without changing the width of the compasses, put the sharp end of the compasses at R and draw an arc on the other side of AB compared with P. Do the same at S and make sure that the second arc intersects the first arc. Step 3 : Draw a line from P to the point of intersection. This line passes through point P and is perpendicular to AB. Constructing a perpendicular to a line, through a point not on the line
1. Place compass point on the given point, and draw arc such that it intersects line twice.
2. Place compass on each arc intersection, and draw a further pair of arcs which intersect each other on the other side of line from original point.
3. Using a straight edge, connect this intersection to the original point with a straight line.
How to construct a perpendicular line from a point to a line?

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