Question

1. consider the diagram.

which construction does the diagram model?
a. angle bisector
b. duplication of an angle
c. midpoint
d. perpendicular bisector

Explanation:

To determine the construction, we analyze each option:

• Option A (Angle Bisector): The diagram shows an arc intersecting the sides of the angle and a ray from the vertex, which is consistent with the steps to bisect an angle (drawing an arc from the vertex, then arcs from the intersection points to find the bisector).
• Option B (Duplication of an Angle): Duplicating an angle involves constructing a congruent angle at a different vertex, which is not shown here.
• Option C (Midpoint): Midpoint construction is for segments, not angles, so this is irrelevant.
• Option D (Perpendicular Bisector): Perpendicular bisector is for segments, not angles, so this is incorrect.

The diagram’s elements (arc from vertex \( C \), intersection with sides, and a ray from \( C \)) match the angle bisector construction.

Answer:

A. Angle Bisector