Perpendicular Bisector

 

To bisect a line is to cut a line segment into two equal parts at 90°.

The bisector can either cross the line segment it bisects, or can be a line segment or ray that ends at the line, as shown below. 

 

A perpendicular bisector is a line that cuts a line segment connected by two points exactly in half by a 90 degree angle.  

 

Demonstration

Step 1: Draw a line segment AB.

Step 2: With A as center draw a circle using compass.

Note : The radius of the circle must be more than half length of  AB.

Step 3: With same radius, but B as the center point draw another circle. Now both the circles will intersect at a point.

Name the intersecting points as C and D. Draw a line from C to D. The line CD will cut the line AB at a point O.

Step 4: Verify using a ruler that O is the midpoint of line AB. Also measure the angles COA and COB. You will arrive at measuring them as right angles.

Therefore, CD is the perpendicular bisector of AB.