Construction of perpendicular bisector of a line segment

Construction of perpendicular bisector of a line segment

In earlier class, we learnt about perpendicular lines. Observe the Fig.5.24.

These are perpendicular lines. In both the cases the perpendicular line l divides both the line segments into two equal parts. This line is called perpendicular bisector of the line segment. So, a perpendicular line which divides a line segment into two equal parts is a perpendicular bisector of the given line segment.

Now we are going to learn, how to construct a perpendicular bisector to a given line segment.

Example 5.11 

Construct a perpendicular bisector of the line segment AB = 6 cm.

Step 1: Draw a line. Mark two points A and B on it so that AB = 6 cm.

Step 2: Using compass with A as center and radius more than half of the length of AB, draw two arcs of same length, one above AB and one below AB.

Step 3: With the same radius and B as center draw two arcs to cut the arcs drawn in step 2. Mark the points of intersection of the arcs as C and D

Step 4: Join C and D. CD will intersect AB. Mark the point of intersection as O

CD is the required perpendicular bisector of AB.

Measure ∠AOC. Measure the length of AO and OB. What do you observe?

Think

1. What will happen if the radius of the arc is less than half of AB?