Exercise 14 Page 46

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

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

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

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

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