GEOMETRY. OPERATIONS WITH LINE SEGMENTS

2. Operations with Line Segments

2.1. Adding and subtracting line segments

       a) Adding

•  The addition of two segments is another segment that begins at the origin of the first segment and ends  at   the end of the second segment. 
• The length of the new segment is the addition of the measures of those two segments.

      b) Subtracting

• The subtration of two segments is another segment that takes as the origin, the end of the smaller segment and as the end, the end of the biggest segment.
• The length of the segment difference is equal to the subtraction of the lengths of two segments.

2.2. Perpendicular Bisector

• The perpendicular bisector is a perpendicular line that passes through the midpoint of the segment, so it divides the segment in two equal parts.

To draw a line bisector we use the compass and the rulers. Let's check how to draw it with this video:

2.3. How to divide a line segment into equal parts (Thales theorem)

1. Draw a ray that shares the origin of point A with the line segment segment AB.

 

2. Mark in the ray as many equal units as you want to obtain starting from point A. In this case, we are goint to divide the segment into three equal parts.

 

3. Join the point B with the end of the ray. For each of the divisions of the ray, draw parallel lines to the segment joining B. The points obtained in the segment AB represent 3 equal parts.

 

If you have any doubt about the process, you can watch this video: