Question

construction you are given $overline{ab}$ as shown. you are asked to use a compass and straightedge to construct a perpendicular bisector of $overline{ab}$. which diagram shows a valid approach to this construction?

Explanation:

Step1: Recall construction steps

To construct a perpendicular bisector of a line - segment $\overline{AB}$ using a compass and straight - edge, we first set the compass width to more than half the length of $\overline{AB}$. Then, with the compass centered at point $A$, we draw arcs above and below the line - segment. Next, without changing the compass width, we center the compass at point $B$ and draw arcs above and below the line - segment, intersecting the previous arcs. Finally, we use the straight - edge to draw a line through the intersection points of the arcs. This line is the perpendicular bisector of $\overline{AB}$.

Step2: Analyze diagrams

We look for a diagram that shows arcs drawn from both endpoints $A$ and $B$ (with the same compass width) above and below the line - segment $\overline{AB}$, and then a line drawn through the intersection points of those arcs.

Answer:

The diagram that shows arcs drawn from both endpoints $A$ and $B$ of the line - segment $\overline{AB}$ (with equal compass width) above and below the line - segment and then a line connecting the intersection points of those arcs is the correct one. Since the diagrams are not labeled, you would identify the one that follows the described construction steps.