Question

1. which diagram below, shows the partial construction for the perpendicular bisector of ab? 7. the diagram below shows the construction of the bisector of ∠abc.

Explanation:

Step1: Recall perpendicular - bisector construction

To construct the perpendicular bisector of a line segment $\overline{AB}$, we start by placing the compass at one - end point (say $A$) and draw an arc with a radius greater than $\frac{1}{2}AB$. Then we place the compass at the other end - point ($B$) and draw an arc with the same radius. The two arcs intersect at two points, and the line joining these two intersection points is the perpendicular bisector of $\overline{AB}$.

Step2: Analyze the given diagrams

In the correct construction of the perpendicular bisector of $\overline{AB}$, we should have two arcs drawn from $A$ and $B$ with the same radius intersecting at two points. The top - most diagram shows two circles centered at points on the sides of an angle, which is a construction for the angle bisector of an angle (not the perpendicular bisector of a line segment). The middle diagram shows two circles centered at $A$ and $B$ intersecting at two points above and below the line segment $\overline{AB}$, which is the correct partial construction for the perpendicular bisector of $\overline{AB}$. The bottom - most diagram shows a single circle centered at a point $C$ intersecting the line segment $\overline{AB}$, which is not the correct way to start the perpendicular - bisector construction.

Answer:

The middle diagram