Step  Manipulative  Description  Justification 


Line segment AB is the line segment to bisect. 
These are the criteria. 
1 

Draw a circle with center A and radius AB. 
Euclid
Elements Book 1 Postulate 3: A circle can be draw with any center and any radius.

2 

Draw a circle with center B and radius BA. 
Euclid
Elements Book 1 Postulate 3: A circle can be draw with any center and any radius.

3 

Mark the intersections of the circles as points C and D. 
An intersection is a point of concurrency. 
4 

Draw a line through points C and D. This line is the
perpendicular bisector. 
Euclid. Elements
Book 1 Postulate 1. A line can be drawn from any point to any point.

5 

The intersection of line segment AB and line segment CD is the midpoint
of line segment AB

An intersection is a point of concurrency. 
Table 1: Constructing a perpendicular bisector. 