Question

1. this figure represents a step in a compass-and-straightedge construction. identify the construction.

a perpendicular bisector

a congruent angle

an angle bisector

a congruent line segment

Explanation:

To identify the construction, we analyze each option:

• A perpendicular bisector construction involves creating a line that is perpendicular to a segment and bisects it. The figure shows a step where a compass arc intersects a line (A'B') and has another arc, which is consistent with the initial steps of constructing a perpendicular bisector (drawing arcs from a point on the line to find a perpendicular line).
• A congruent angle construction focuses on replicating an angle, which isn't shown here (no original angle to copy).
• An angle bisector splits an existing angle, but there's no angle to bisect in the figure.
• A congruent line segment construction is about copying a segment, not what's depicted here.

So the construction is a perpendicular bisector.

Answer:

a perpendicular bisector