Exercise 13 Page 46

We want to construct the perpendicular bisector of line segment $\overline{AB}.$

To start, we should put the compass point on point $A$ and draw an arc. The opening of the compass must be greater than $\frac{1}{2}AB$ — it must go further than the midpoint between $A$ and $B.$ Otherwise, the arcs we draw will not intersect.

With the same compass setting, we will put the compass point on point $B$ and draw another arc. We will label the points where the two arcs intersect as $C$ and $D.$

Finally, we will draw $\overleftrightarrow{CD}.$ The point of intersection $\overleftrightarrow{CD}$ and $\overline{AB}$ is the midpoint $M$ of $\overline{AB}.$

Since $\overleftrightarrow{CD}$ is perpendicular to $\overline{AB}$ at midpoint $M,$ it is the perpendicular bisector of $\overline{AB}.$