Question

use the compass and ruler to construct the perpendicular bisector of the line segment $\overline{ab}$.

Explanation:

Step1: Set compass at A

Set the compass width greater than half of \( \overline{AB} \). Draw arcs above and below \( \overline{AB} \).

Step2: Set compass at B

Using the same compass width, draw arcs above and below \( \overline{AB} \) that intersect the previous arcs.

Step3: Draw the bisector

Use the ruler to draw a line through the intersection points of the arcs. This line is the perpendicular bisector of \( \overline{AB} \).

Answer:

The perpendicular bisector is constructed by following the steps of drawing arcs from A and B (with compass width > \( \frac{1}{2}AB \)) and connecting their intersection points with a ruler.