### 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 \(\overline {AB}\)

**Make a note of the following steps to construct a perpendicular bisector of the line segment \(AB = 10 cm\).**

**The construction of perpendicular bisector of a line segment**

**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 \(AO\) \(= OB\) \(= 5 cm\).