# FUNDAMENTAL CONSTRUCTIONS

## 1. LINE BISECTOR

The line bisector is a perpendicular line which divides the segment in two equal parts.

STEPS:

First of all we need to draw a segment. We will call it AB.

1. Put your compass in point A, open it almost to the middle of the segment AB, and draw an arc.
2. Do the same from dot B, where the arcs cross each other we get points 1 and 2.
3. Join 1 and 2, and this way we get the line bisector.

## 2. PERPENDICULAR TO A POINT ON A LINE

The perpendicular to a point on a line is a line which crosses another line forming a right angle (90º) on a given point of that line.

STEPS:

1. Draw a line (r) and mark a point (A) on it.
2. Put your compass in the given point A and draw an arc with the measure you want, where the arc crosses the line we get 1 and 2.
3. Get the line bisector between 1 and 2.
4. Join 3 and 4, and this way we get the perpendicular to the line on point A.

## 3. PERPENDICULAR TO A POINT OUTSIDE A LINE

The perpendicular to a point outside a line is another line which crosses the first line forming a right angle (90º) on a given point outside it.

The point can be above or below the line and we will follow the same steps.

STEPS:

1. Draw a line (r) and mark a point (A) above or below it.
2. Put your compass in the given point A and draw an arc with the measure you want, where the arc crosses the line we get 1 and 2.
3. Get the line bisector between 1 and 2.
4. Join 3 and 4, and this way we get the perpendicular to the line on point A.

## 4. PERPENDICULAR TO A RAY (TO ONE END OF LINE)

STEPS:

1. Draw a ray.
2. Put your compass in point A, draw an arc, and where it crosses the line we get point 1.
3. Put your compass in point 1 with the same measure and draw an arc, where it crosses the previous one we get point 2.
4. Put your compass in point 2 with the same measure and draw an arc, where it crosses the previous arc we get point 3.
5. Put your compass in point 2 and 3 with the same measure and draw two arcs where these arcs cross we get point 4.
6. If we join point 4 with the given point A we get the perpendicular line.