### Theory:

Bisecting means dividing a line segment into two equal parts.

Perpendicular bisector:
When a line segment is divided into two halves by a perpendicular line segment, then the perpendicular line segment becomes the perpendicular bisector.

In the figure given above, $$\overline {CD}$$ is the perpendicular bisector of $$\overline {AB}$$
The construction of perpendicular bisector of a line segment
Make a note of the following steps to construct a perpendicular bisector of the line segment $$AB = 10 cm$$.

Step 1: Draw a line and mark two points $$A$$ and $$B$$ on it. That is, $$AB = 10cm$$.

Step 2: Make $$A$$ as centre 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: Now take $$B$$ as centre, draw two arcs with the same radius to cut the arcs drawn in step $$2$$. Mark the points of intersection of the arcs as $$C$$ and $$D$$.

Step 4: Then, join $$C$$ and $$D$$. The line $$CD$$ will intersect $$AB$$. Mark the point of intersection as $$O$$. $$CD$$ is the required perpendicular bisector of $$AB$$. Now measure the distance between $$A$$ and $$O$$ and $$O$$ and $$B$$. We have $$AO = OB$$ $$= 5 cm$$.

Thus, we have constructed the perpendicular bisector of $$AB$$ and this perpendicular bisector divides the line $$AB =10 cm$$ into two parts, such that $$AO$$ $$= OB$$ $$= 5 cm$$.