Question

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

Explanation:

Step1: Set compass width

Open the compass to a width greater than half the length of $\overline{AB}$.

Step2: Draw arcs from A

With the compass centered at point $A$, draw arcs above and below the line - segment $\overline{AB}$.

Step3: Draw arcs from B

Without changing the compass width, center the compass at point $B$ and draw arcs above and below the line - segment $\overline{AB}$ to intersect the previous arcs.

Step4: Draw the perpendicular bisector

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

Answer:

The constructed line through the intersection points of the arcs is the perpendicular bisector of $\overline{AB}$.