Question

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

Explanation:

Step1: Set compass width

Open the compass to a width greater than half of \( \overline{AB} \). Place the compass point on \( A \) and draw an arc above and below \( \overline{AB} \).

Step2: Draw arc from B

Keep the compass width the same. Place the compass point on \( B \) and draw arcs intersecting the previous arcs at two points, say \( C \) and \( D \).

Step3: Draw the bisector

Use the ruler to draw a line through \( C \) and \( D \). This line is the perpendicular bisector of \( \overline{AB} \).

Answer:

The perpendicular bisector is constructed as described (with a line through the intersection points of the arcs centered at A and B).