Question

which geometric construction is shown in the diagram? a perpendicular segment bisector b perpendicular line through a point on the line c perpendicular line through a point not on the line d angle bisector

Explanation:

Step1: Recall geometric construction features

In the diagram, we have two arcs drawn from points A and B on a line segment. The intersection of these arcs is used to draw a line. This is the construction method for a perpendicular segment bisector. A perpendicular segment bisector divides a line - segment into two equal parts and is perpendicular to the line - segment.

Step2: Analyze each option

• Option A: The construction shown is for a perpendicular segment bisector. We construct arcs from the endpoints of the segment and join the intersection points of the arcs to get the perpendicular bisector.
• Option B: To construct a perpendicular line through a point on the line, we use a different set of steps involving a single - point on the line and arcs around that point.
• Option C: For constructing a perpendicular line through a point not on the line, the construction process is different from the one shown.
• Option D: An angle bisector construction is for dividing an angle into two equal angles, which is not related to the given diagram.

Answer:

A. Perpendicular Segment Bisector