Question

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

Explanation:

Step1: Set compass at A

Open compass to a length 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 a 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 arc - drawing from A and B (with compass width > half of \( \overline{AB} \)) and then connecting the arc - intersection points with a ruler.